## Zelik, Sergey V.

Compute Distance To:
 Author ID: zelik.sergey-v Published as: Zelik, Sergey; Zelik, S. V.; Zelik, S.; Zelik, Sergey V.; Zelik, Sergeĭ V.
 Documents Indexed: 127 Publications since 1994, including 1 Book Reviewing Activity: 84 Reviews Co-Authors: 48 Co-Authors with 101 Joint Publications 1,368 Co-Co-Authors
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### Co-Authors

 23 single-authored 21 Miranville, Alain M. 17 Efendiev, Messoud 14 Ilyin, Alexei A. 11 Pata, Vittorino 9 Kalantarov, Varga K. 8 Chepyzhov, Vladimir V. 8 Kostianko, Anna 6 Schimperna, Giulio 6 Vishik, Marko Iosifovich 5 Laptev, Ari 4 Grasselli, Maurizio 4 Mielke, Alexander 4 Segatti, Antonio 3 Eden, Alp 3 Gatti, Stefania 3 Turaev, Dmitry V. 2 Bridges, Thomas J. 2 Cherfils, Laurence 2 Fabrie, Pierre 2 Galusinski, Cédric 2 Sun, Chunyou 1 Anthony, Peter 1 Bartuccelli, Michele V. 1 Berestycki, Henri 1 Bilgin, Bilgesu Arif 1 Busca, Jérôme 1 Deane, Jonathan H. B. 1 di Plinio, Francesco 1 Eberl, Hermann J. 1 Fuhrmann, Jürgen 1 Gajewski, Herbert 1 Galbally, Benjamin 1 Kostianko, A. G. 1 Kostyanko, A. G. 1 Li, Xinhua 1 Lloyd, David J. B. 1 Loss, Michael 1 Mei, Xinyu 1 Patni, Kavita 1 Pennant, Jon 1 Pennant, Jonathan 1 Rossides, Tasos 1 Rykov, Yuri 1 Savostianov, Anton 1 Savostianov, Anton K. 1 Shirikyan, Armen R. 1 Titi, Edriss Saleh 1 Warner, Christopher
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### Serials

 13 Communications on Pure and Applied Analysis 8 Mathematical Notes 7 Mathematical Methods in the Applied Sciences 7 Discrete and Continuous Dynamical Systems 6 Nonlinearity 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Russian Mathematical Surveys 4 Mathematische Nachrichten 4 Doklady Mathematics 4 Discrete and Continuous Dynamical Systems. Series B 3 Physica D 3 Asymptotic Analysis 3 Journal of Dynamics and Differential Equations 3 Sbornik: Mathematics 3 Journal of Mathematical Fluid Mechanics 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Physics 2 Journal of Differential Equations 2 Transactions of the American Mathematical Society 2 Advances in Differential Equations 2 Journal of Evolution Equations 1 Archive for Rational Mechanics and Analysis 1 Rocky Mountain Journal of Mathematics 1 Applied Mathematics and Optimization 1 Glasgow Mathematical Journal 1 Hokkaido Mathematical Journal 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the Moscow Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Journal of Scientific Computing 1 Mathematica Bohemica 1 IMRN. International Mathematics Research Notices 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Advances in Mathematical Sciences and Applications 1 Electronic Journal of Differential Equations (EJDE) 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Regular and Chaotic Dynamics 1 Annales Henri Poincaré 1 Nonlinear Boundary Value Problems 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Milan Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bulletin of Mathematical Sciences 1 Stochastic and Partial Differential Equations. Analysis and Computations
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### Fields

 122 Partial differential equations (35-XX) 47 Dynamical systems and ergodic theory (37-XX) 11 Fluid mechanics (76-XX) 5 Real functions (26-XX) 5 Ordinary differential equations (34-XX) 5 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 3 Operator theory (47-XX) 2 Measure and integration (28-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Number theory (11-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

109 Publications have been cited 2,096 times in 1,029 Documents Cited by Year
Attractors for dissipative partial differential equations in bounded and unbounded domains. Zbl 1221.37158
Miranville, A.; Zelik, S.
2008
Exponential attractors for a nonlinear reaction-diffusion system in $$\mathbb R^3$$. Zbl 1151.35315
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2000
The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2011
Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113
Miranville, Alain; Zelik, Sergey
2004
Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011
Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey
2004
Smooth attractors for strongly damped wave equations. Zbl 1113.35023
Pata, Vittorino; Zelik, Sergey
2006
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005
Efendiev, M.; Zelik, S.; Miranville, A.
2005
The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Zbl 1041.35016
Efendiev, M. A.; Zelik, S. V.
2001
Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020
Miranville, A.; Zelik, S.
2005
Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053
Kalantarov, Varga; Zelik, Sergey
2009
Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168
Zelik, Sergey
2004
Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2004
The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046
Miranville, Alain; Zelik, Sergey
2010
A result on the existence of global attractors for semigroups of closed operators. Zbl 1152.47046
Pata, Vittorino; Zelik, Sergey
2007
On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086
Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey
2009
Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. Zbl 1133.35017
Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2007
Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity. Zbl 1025.37044
Zelik, Sergey V.
2003
A remark on the damped wave equation. Zbl 1140.35533
Pata, Vittorino; Zelik, Sergey
2006
Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054
Kalantarov, Varga K.; Zelik, Sergey
2012
Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055
Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey
2016
On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160
Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey
2009
Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024
Miranville, Alain; Zelik, Sergey
2002
On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2014
Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018
Zelik, Sergey
2004
The attractor for a nonlinear hyperbolic equation in the unbounded domain. Zbl 1153.35311
Zelik, S. V.
2001
Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038
Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey
2010
Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003
Zelik, Sergey; Mielke, Alexander
2009
Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070
Gatti, S.; Miranville, A.; Pata, V.; Zelik, S.
2008
Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092
Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V.
2011
Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067
Zelik, Sergey
2007
Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027
Efendiev, M.; Zelik, S.
2008
Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039
Zelik, Sergey
2014
Strong trajectory attractor for a dissipative reaction-diffusion system. Zbl 1227.35084
Vishik, M. I.; Zelik, S. V.; Chepyzhov, V. V.
2010
Existence and longtime behavior of a biofilm model. Zbl 1175.35017
Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J.
2009
Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038
Efendiev, M.; Zelik, S.
2002
Infinite energy solutions for damped Navier-Stokes equations in $${\mathbb{R}^2}$$. Zbl 1293.35221
Zelik, Sergey
2013
Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030
Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2007
The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov’s $$\varepsilon$$-entropy. Zbl 0989.35032
Zelik, S. V.
2001
On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036
Mielke, Alexander; Zelik, Sergey
2014
On the strongly damped wave equation with memory. Zbl 1149.35015
di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey
2008
Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain. Zbl 1258.35036
Efendiev, M. A.; Zelik, S. V.
2002
Exponential attractors for random dynamical systems and applications. Zbl 1320.35089
Shirikyan, Armen; Zelik, Sergey
2013
Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054
Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2010
Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations. Zbl 1178.34060
Efendiev, M.; Zelik, S.
2009
Global and exponential attractors for 3-D wave equations with displacement dependent damping. Zbl 1101.35020
Pata, Vittorino; Zelik, Sergey
2006
The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging. Zbl 1030.35016
Efendiev, M.; Zelik, S.
2003
Attractors and their regularity for 2-D wave equations with nonlinear damping. Zbl 1145.35045
Pata, Vittorino; Zelik, Sergey
2007
Global averaging and parametric resonances in damped semilinear wave equations. Zbl 1114.35131
Zelik, S.
2006
Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185
Savostianov, Anton; Zelik, Sergey
2014
Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056
Kostianko, Anna; Zelik, Sergey
2015
Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2003
A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366
Gatti, Stefania; Pata, Vittorino; Zelik, Sergey
2009
Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081
Eden, A.; Zelik, S. V.; Kalantarov, V. K.
2013
Regular attractors and nonautonomous perturbations of them. Zbl 1278.35027
Vishik, Marko I.; Zelik, Sergey V.; Chepyzhov, Vladimir V.
2013
Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus. Zbl 1297.35010
Bartuccelli, Michele; Deane, Jonathan; Zelik, Sergey
2013
Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045
Efendiev, M.; Miranville, A.; Zelik, S.
2004
Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068
Miranville, A.; Zelik, S.
2009
Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014
Zelik, Sergey
2015
Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043
Kostianko, Anna; Zelik, Sergey
2017
Multiparameter semigroups and attractors of reaction-diffusion equations in $$\mathbb R^n$$. Zbl 1176.37025
Zelik, S. V.
2004
Recent progress in attractors for quintic wave equations. Zbl 1349.35040
Savostianov, Anton; Zelik, Sergey
2014
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
2016
Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains. Zbl 1125.35052
Zelik, S. V.
2007
Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains. Zbl 1149.37328
Efendiev, M.; Miranville, A.; Zelik, S.
2004
Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156
Savostianov, Anton; Zelik, Sergey
2016
Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains. Zbl 1315.35039
Eden, A.; Kalantarov, V. K.; Zelik, S. V.
2014
Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052
Schimperna, Giulio; Zelik, Sergey
2013
Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in $$\mathbb R^3$$. Zbl 1264.35055
Zelik, Sergey; Pennant, Jon
2013
Regular attractor for a nonlinear elliptic system in a cylindrical domain. Zbl 0940.35085
Vishik, M. I.; Zelik, S. V.
1999
Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129
Zelik, Sergey
2008
Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151
Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey
2012
Infinite-dimensional trajectory attractors of elliptic boundary value problems in cylindrical domains. Zbl 1049.37048
Mielke, A.; Zelik, S. V.
2002
Infinite energy solutions for dissipative Euler equations in $$\mathbb{R}^2$$. Zbl 1325.35137
2015
Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Zbl 1133.35023
Miranville, A.; Zelik, S.
2007
Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials. Zbl 1284.35085
Eden, A.; Kalantarov, V. K.; Zelik, S. V.
2013
Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Zbl 1297.35164
Anthony, Peter; Zelik, Sergey
2014
The finite dimensional attractor for a 4th order system of Cahn-Hilliard type with a supercritical nonlinearity. Zbl 1035.35019
Efendiev, M. A.; Gajewski, H.; Zelik, S.
2002
Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033
Kostianko, Anna; Zelik, Sergey
2018
An attractor of a nonlinear system of reaction-diffusion equations in $$\mathbb{R}^n$$ and estimates of its $$\varepsilon$$-entropy. Zbl 0948.35016
Zelik, S. V.
1999
Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in $$\mathbb R^3$$. Zbl 1338.35064
Savostianov, Anton; Zelik, Sergey
2016
Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051
Zelik, S. V.; Ilyin, A. A.
2014
Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173
Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey
2019
Upper bounds for the attractor dimension of damped Navier-Stokes equations in $$\mathbb R^2$$. Zbl 1327.35036
Ilyin, Alexei; Patni, Kavita; Zelik, Sergey
2016
Analytical proof of space-time chaos in Ginzburg-Landau equations. Zbl 1213.35376
Turaev, Dmitry; Zelik, Sergey
2010
Large dispersion, averaging and attractors: three 1D paradigms. Zbl 1406.35061
Kostianko, Anna; Titi, Edriss; Zelik, Sergey
2018
On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146
Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey
2016
The trajectory attractor of a nonlinear elliptic system in a cylindrical domain. Zbl 0871.35016
Vishik, M. I.; Zelik, S. V.
1996
Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions. Zbl 1398.35145
Chepyzhov, Vladimir; Ilyin, Alexei; Zelik, Sergey
2018
Strong trajectory and global $$\mathbf{W^{1,p}}$$-attractors for the damped-driven Euler system in $$\mathbb R^2$$. Zbl 1359.35013
Zelik, Sergey; Ilyin, Alexei; Chepyzhov, Vladimir
2017
A note on a strongly damped wave equation with fast growing nonlinearities. Zbl 1312.35134
Kalantarov, Varga; Zelik, Sergey
2015
Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in $$\mathbb{R}^n$$. Zbl 1125.35012
Mielke, Alexander; Zelik, Sergey V.
2007
The attractor of a quasilinear hyperbolic equation with dissipation in $$\mathbb{R}^n$$: Dimension and $$\varepsilon$$-entropy. Zbl 0974.35016
Zelik, S. V.
2000
Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080
Savostianov, Anton K.; Zelik, Sergeĭ V.
2020
Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147
Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey
2018
Formally gradient reaction-diffusion systems in $$\mathbb{R}^n$$ have zero spatio-temporal topological entropy. Zbl 1058.35089
Zelik, S.
2003
Classification of positive solutions of semilinear elliptic equations. Zbl 1048.35020
Busca, Jérôme; Efendiev, Messoud; Zelik, S.
2004
Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations. Zbl 1308.35240
Bridges, Thomas; Pennant, Jonathan; Zelik, Sergey
2014
Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Zbl 1304.35127
Vishik, Mark I.; Zelik, Sergey
2014
Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101
Ilyin, Alexei A.; Zelik, Sergey
2021
Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential. Zbl 1184.35070
Segatti, Antonio; Zelik, Sergey
2009
Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101
Ilyin, Alexei A.; Zelik, Sergey
2021
Validity of the hyperbolic Whitham modulation equations in Sobolev spaces. Zbl 1455.35233
Bridges, Thomas J.; Kostianko, Anna; Zelik, Sergey
2021
Infinite energy solutions for weakly damped quintic wave equations in $$\mathbb{R}^3$$. Zbl 1460.35040
Mei, Xinyu; Savostianov, Anton; Sun, Chunyou; Zelik, Sergey
2021
Sharp dimension estimates for the attractors of the regularized damped Euler system. Zbl 1477.35149
Zelik, S. V.; Ilyin, A. A.; Kostianko, A. G.
2021
Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080
Savostianov, Anton K.; Zelik, Sergeĭ V.
2020
Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196
Ilyin, Alexei; Laptev, Ari; Zelik, Sergey
2020
Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173
Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey
2019
On the Lieb-Thirring constant on the torus. Zbl 1436.35268
Zelik, S. V.; Ilyin, A. A.; Laptev, A. A.
2019
Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033
Kostianko, Anna; Zelik, Sergey
2018
Large dispersion, averaging and attractors: three 1D paradigms. Zbl 1406.35061
Kostianko, Anna; Titi, Edriss; Zelik, Sergey
2018
Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions. Zbl 1398.35145
Chepyzhov, Vladimir; Ilyin, Alexei; Zelik, Sergey
2018
Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147
Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey
2018
Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043
Kostianko, Anna; Zelik, Sergey
2017
Strong trajectory and global $$\mathbf{W^{1,p}}$$-attractors for the damped-driven Euler system in $$\mathbb R^2$$. Zbl 1359.35013
Zelik, Sergey; Ilyin, Alexei; Chepyzhov, Vladimir
2017
Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055
Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey
2016
One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016
Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey
2016
Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156
Savostianov, Anton; Zelik, Sergey
2016
Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in $$\mathbb R^3$$. Zbl 1338.35064
Savostianov, Anton; Zelik, Sergey
2016
Upper bounds for the attractor dimension of damped Navier-Stokes equations in $$\mathbb R^2$$. Zbl 1327.35036
Ilyin, Alexei; Patni, Kavita; Zelik, Sergey
2016
On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146
Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey
2016
Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056
Kostianko, Anna; Zelik, Sergey
2015
Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014
Zelik, Sergey
2015
Infinite energy solutions for dissipative Euler equations in $$\mathbb{R}^2$$. Zbl 1325.35137
2015
A note on a strongly damped wave equation with fast growing nonlinearities. Zbl 1312.35134
Kalantarov, Varga; Zelik, Sergey
2015
On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2014
Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039
Zelik, Sergey
2014
On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036
Mielke, Alexander; Zelik, Sergey
2014
Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185
Savostianov, Anton; Zelik, Sergey
2014
Recent progress in attractors for quintic wave equations. Zbl 1349.35040
Savostianov, Anton; Zelik, Sergey
2014
Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains. Zbl 1315.35039
Eden, A.; Kalantarov, V. K.; Zelik, S. V.
2014
Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Zbl 1297.35164
Anthony, Peter; Zelik, Sergey
2014
Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051
Zelik, S. V.; Ilyin, A. A.
2014
Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations. Zbl 1308.35240
Bridges, Thomas; Pennant, Jonathan; Zelik, Sergey
2014
Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Zbl 1304.35127
Vishik, Mark I.; Zelik, Sergey
2014
Regular attractors of autonomous and nonautonomous dynamical systems. Zbl 1307.37012
Zelik, S. V.; Chepyzhov, V. V.
2014
Infinite energy solutions for damped Navier-Stokes equations in $${\mathbb{R}^2}$$. Zbl 1293.35221
Zelik, Sergey
2013
Exponential attractors for random dynamical systems and applications. Zbl 1320.35089
Shirikyan, Armen; Zelik, Sergey
2013
Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081
Eden, A.; Zelik, S. V.; Kalantarov, V. K.
2013
Regular attractors and nonautonomous perturbations of them. Zbl 1278.35027
Vishik, Marko I.; Zelik, Sergey V.; Chepyzhov, Vladimir V.
2013
Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus. Zbl 1297.35010
Bartuccelli, Michele; Deane, Jonathan; Zelik, Sergey
2013
Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052
Schimperna, Giulio; Zelik, Sergey
2013
Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in $$\mathbb R^3$$. Zbl 1264.35055
Zelik, Sergey; Pennant, Jon
2013
Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials. Zbl 1284.35085
Eden, A.; Kalantarov, V. K.; Zelik, S. V.
2013
Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054
Kalantarov, Varga K.; Zelik, Sergey
2012
Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151
Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey
2012
The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129
Cherfils, Laurence; Miranville, Alain; Zelik, Sergey
2011
Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092
Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V.
2011
The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046
Miranville, Alain; Zelik, Sergey
2010
Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038
Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey
2010
Strong trajectory attractor for a dissipative reaction-diffusion system. Zbl 1227.35084
Vishik, M. I.; Zelik, S. V.; Chepyzhov, V. V.
2010
Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054
Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2010
Analytical proof of space-time chaos in Ginzburg-Landau equations. Zbl 1213.35376
Turaev, Dmitry; Zelik, Sergey
2010
Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053
Kalantarov, Varga; Zelik, Sergey
2009
On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086
Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey
2009
On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160
Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey
2009
Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003
Zelik, Sergey; Mielke, Alexander
2009
Existence and longtime behavior of a biofilm model. Zbl 1175.35017
Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J.
2009
Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations. Zbl 1178.34060
Efendiev, M.; Zelik, S.
2009
A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366
Gatti, Stefania; Pata, Vittorino; Zelik, Sergey
2009
Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068
Miranville, A.; Zelik, S.
2009
Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential. Zbl 1184.35070
Segatti, Antonio; Zelik, Sergey
2009
Attractors for dissipative partial differential equations in bounded and unbounded domains. Zbl 1221.37158
Miranville, A.; Zelik, S.
2008
Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070
Gatti, S.; Miranville, A.; Pata, V.; Zelik, S.
2008
Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027
Efendiev, M.; Zelik, S.
2008
On the strongly damped wave equation with memory. Zbl 1149.35015
di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey
2008
Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129
Zelik, Sergey
2008
A result on the existence of global attractors for semigroups of closed operators. Zbl 1152.47046
Pata, Vittorino; Zelik, Sergey
2007
Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. Zbl 1133.35017
Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2007
Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067
Zelik, Sergey
2007
Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030
Miranville, Alain; Pata, Vittorino; Zelik, Sergey
2007
Attractors and their regularity for 2-D wave equations with nonlinear damping. Zbl 1145.35045
Pata, Vittorino; Zelik, Sergey
2007
Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains. Zbl 1125.35052
Zelik, S. V.
2007
Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Zbl 1133.35023
Miranville, A.; Zelik, S.
2007
Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in $$\mathbb{R}^n$$. Zbl 1125.35012
Mielke, Alexander; Zelik, Sergey V.
2007
Smooth attractors for strongly damped wave equations. Zbl 1113.35023
Pata, Vittorino; Zelik, Sergey
2006
A remark on the damped wave equation. Zbl 1140.35533
Pata, Vittorino; Zelik, Sergey
2006
Global and exponential attractors for 3-D wave equations with displacement dependent damping. Zbl 1101.35020
Pata, Vittorino; Zelik, Sergey
2006
Global averaging and parametric resonances in damped semilinear wave equations. Zbl 1114.35131
Zelik, S.
2006
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005
Efendiev, M.; Zelik, S.; Miranville, A.
2005
Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020
Miranville, A.; Zelik, S.
2005
Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113
Miranville, Alain; Zelik, Sergey
2004
Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011
Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey
2004
Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168
Zelik, Sergey
2004
Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2004
Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018
Zelik, Sergey
2004
Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045
Efendiev, M.; Miranville, A.; Zelik, S.
2004
Multiparameter semigroups and attractors of reaction-diffusion equations in $$\mathbb R^n$$. Zbl 1176.37025
Zelik, S. V.
2004
Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains. Zbl 1149.37328
Efendiev, M.; Miranville, A.; Zelik, S.
2004
Classification of positive solutions of semilinear elliptic equations. Zbl 1048.35020
Busca, Jérôme; Efendiev, Messoud; Zelik, S.
2004
The long-time behaviour of the thermoconvective flow in a porous medium. Zbl 1156.37323
Efendiev, M. A.; Fuhrmann, J.; Zelik, S. V.
2004
Dynamical approach for positive solutions of semilinear elliptic problems in unbounded domains. Zbl 1107.35349
Berestycki, H.; Efendiev, M.; Zelik, S.
2004
Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity. Zbl 1025.37044
Zelik, Sergey V.
2003
The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging. Zbl 1030.35016
Efendiev, M.; Zelik, S.
2003
Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043
Efendiev, Messoud; Miranville, Alain; Zelik, Sergey
2003
Formally gradient reaction-diffusion systems in $$\mathbb{R}^n$$ have zero spatio-temporal topological entropy. Zbl 1058.35089
Zelik, S.
2003
Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024
Miranville, Alain; Zelik, Sergey
2002
Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038
Efendiev, M.; Zelik, S.
2002
Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain. Zbl 1258.35036
Efendiev, M. A.; Zelik, S. V.
2002
Infinite-dimensional trajectory attractors of elliptic boundary value problems in cylindrical domains. Zbl 1049.37048
Mielke, A.; Zelik, S. V.
2002
The finite dimensional attractor for a 4th order system of Cahn-Hilliard type with a supercritical nonlinearity. Zbl 1035.35019
Efendiev, M. A.; Gajewski, H.; Zelik, S.
2002
...and 9 more Documents
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### Cited by 898 Authors

 79 Miranville, Alain M. 58 Zelik, Sergey V. 37 Grasselli, Maurizio 32 Zhong, Chengkui 30 Pata, Vittorino 27 Yang, Zhijian 26 Gal, Ciprian Gheorghe Sorin 24 Zhou, Shengfan 23 Sun, Chunyou 22 Conti, Monica C. 21 Chepyzhov, Vladimir V. 21 Colli, Pierluigi 21 Schimperna, Giulio 19 Efendiev, Messoud 18 Gatti, Stefania 15 Cherfils, Laurence 15 Ilyin, Alexei A. 15 Wu, Hao 14 Gilardi, Gianni 13 Cholewa, Jan W. 13 Kalantarov, Varga K. 13 Rocca, Elisabetta 12 Scarpa, Luca 11 Eberl, Hermann J. 11 Giorgini, Andrea 11 Kasyanov, Pavlo O. 11 Meng, Fengjuan 11 Nolasco de Carvalho, Alexandre 11 Sonner, Stefanie 10 Kloeden, Peter Eris 10 Quintanilla de Latorre, Ramón 10 Shomberg, Joseph L. 10 Sprekels, Jürgen 10 Yang, Meihua 9 Bonfoh, Ahmed S. 9 Caraballo Garrido, Tomás 9 Khanmamedov, Azer Kh. 9 Kostianko, Anna 9 Langa, Jose’ Antonio 9 Ma, To Fu 9 Rodríguez-Bernal, Aníbal 9 Yang, Lu 9 Zhao, Caidi 8 Fakih, Hussein 8 Laptev, Ari 8 Robinson, James Cooper 8 Valero, José 8 Vishik, Marko Iosifovich 8 Xie, Yongqin 8 You, Bo 7 Chueshov, Igor’ Dmitrievich 7 Cui, Hongyong 7 Ding, Pengyan 7 Gorban, Nataliia V. 7 Lam, Kei Fong 7 Lasiecka, Irena 7 Li, Xiaojun 7 Liu, Zhiming 7 Marchini, Elsa Maria 7 Nguyen Huy Tuan 7 Pražák, Dalibor 7 Qin, Yuming 7 Segatti, Antonio 7 Wang, Yonghai 7 Webster, Justin T. 7 Yue, Gaocheng 6 Czaja, Radosław 6 Dlotko, Tomasz W. 6 Geredeli, Pelin Guven 6 Goubet, Olivier 6 Li, Yanan 6 Liu, Cuncai 6 Mohan, Manil Thankamani 6 Niu, Weisheng 6 Pierre, Morgan 6 Rossi, Riccarda 6 Wang, Zhaojuan 6 Zhang, Jin 6 Zhao, Chunxiang 6 Zhao, Xiaopeng 6 Zhu, Kaixuan 5 Chechkin, Gregory Aleksandrovich 5 Coti Zelati, Michele 5 Dell’Oro, Filippo 5 Feng, Na 5 Frigeri, Sergio 5 Fukao, Takeshi 5 Gallay, Thierry 5 Ghasemi, Maryam 5 Li, Ke 5 Li, Yangrong 5 Makki, Ahmad 5 Marín-Rubio, Pedro 5 Marinoschi, Gabriela 5 Petzeltová, Hana 5 Signori, Andrea 5 Slijepčević, Siniša 5 Titi, Edriss Saleh 5 Wang, Cheng 5 Wise, Steven M. ...and 798 more Authors
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### Cited in 211 Serials

 70 Journal of Differential Equations 63 Journal of Mathematical Analysis and Applications 61 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 45 Communications on Pure and Applied Analysis 44 Discrete and Continuous Dynamical Systems. Series B 33 Discrete and Continuous Dynamical Systems 25 Applied Mathematics and Optimization 22 Nonlinear Analysis. Real World Applications 21 Mathematical Methods in the Applied Sciences 19 Journal of Mathematical Physics 18 Applicable Analysis 18 Journal of Dynamics and Differential Equations 18 Evolution Equations and Control Theory 16 Physica D 15 Applied Mathematics Letters 15 Journal of Evolution Equations 13 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 12 Nonlinearity 12 SIAM Journal on Mathematical Analysis 12 Journal of Nonlinear Science 11 Applied Mathematics and Computation 11 Asymptotic Analysis 10 Quarterly of Applied Mathematics 10 Discrete and Continuous Dynamical Systems. Series S 9 AIMS Mathematics 8 Archive for Rational Mechanics and Analysis 8 Computers & Mathematics with Applications 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Journal of Applied Analysis and Computation 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Computational and Applied Mathematics 7 Applications of Mathematics 7 Journal of Mathematical Fluid Mechanics 7 Boundary Value Problems 6 Mathematical Notes 6 Chaos, Solitons and Fractals 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 NoDEA. Nonlinear Differential Equations and Applications 6 Acta Mathematica Sinica. English Series 6 Mediterranean Journal of Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Transactions of the American Mathematical Society 5 Acta Applicandae Mathematicae 5 Journal of Scientific Computing 5 European Journal of Applied Mathematics 5 Topological Methods in Nonlinear Analysis 5 Calculus of Variations and Partial Differential Equations 5 Russian Journal of Mathematical Physics 5 Discrete Dynamics in Nature and Society 5 Central European Journal of Mathematics 5 Advances in Difference Equations 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Communications in Mathematical Physics 4 Russian Mathematical Surveys 4 Communications in Partial Differential Equations 4 Doklady Mathematics 4 Abstract and Applied Analysis 4 Stochastics and Dynamics 4 Communications in Computational Physics 4 Mathematical Control and Related Fields 4 Advances in Nonlinear Analysis 3 Journal of Statistical Physics 3 Numerische Mathematik 3 Ricerche di Matematica 3 Zeitschrift für Analysis und ihre Anwendungen 3 Applied Numerical Mathematics 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Electronic Journal of Differential Equations (EJDE) 3 Journal of Difference Equations and Applications 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Communications in Nonlinear Science and Numerical Simulation 3 Dynamical Systems 3 Journal of Applied Mathematics 3 Milan Journal of Mathematics 3 Complex Variables and Elliptic Equations 3 Journal of Elliptic and Parabolic Equations 3 Electronic Research Archive 2 International Journal of Engineering Science 2 Mathematical Biosciences 2 Rocky Mountain Journal of Mathematics 2 Bulletin of Mathematical Biology 2 Annales Polonici Mathematici 2 Czechoslovak Mathematical Journal 2 Glasgow Mathematical Journal 2 Journal of Functional Analysis 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Numerical Analysis 2 Studies in Applied Mathematics 2 Chinese Annals of Mathematics. Series B 2 Stochastic Analysis and Applications 2 Acta Mathematicae Applicatae Sinica. English Series 2 Set-Valued Analysis 2 Opuscula Mathematica 2 Advances in Differential Equations 2 Sbornik: Mathematics 2 Mathematical Problems in Engineering 2 Differential Equations and Dynamical Systems 2 Interfaces and Free Boundaries 2 Journal of the European Mathematical Society (JEMS) 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series ...and 111 more Serials
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### Cited in 38 Fields

 932 Partial differential equations (35-XX) 295 Dynamical systems and ergodic theory (37-XX) 150 Fluid mechanics (76-XX) 81 Mechanics of deformable solids (74-XX) 68 Classical thermodynamics, heat transfer (80-XX) 60 Numerical analysis (65-XX) 46 Biology and other natural sciences (92-XX) 43 Ordinary differential equations (34-XX) 43 Operator theory (47-XX) 42 Probability theory and stochastic processes (60-XX) 38 Calculus of variations and optimal control; optimization (49-XX) 35 Statistical mechanics, structure of matter (82-XX) 31 Integral equations (45-XX) 18 Systems theory; control (93-XX) 17 Global analysis, analysis on manifolds (58-XX) 10 Real functions (26-XX) 8 Computer science (68-XX) 7 Measure and integration (28-XX) 7 Quantum theory (81-XX) 6 Functional analysis (46-XX) 4 Mechanics of particles and systems (70-XX) 4 Geophysics (86-XX) 3 Difference and functional equations (39-XX) 3 General topology (54-XX) 3 Information and communication theory, circuits (94-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Algebraic topology (55-XX) 2 Optics, electromagnetic theory (78-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)