Edit Profile (opens in new tab) Zelik, Sergey V. Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1221.37158Miranville, A.; Zelik, S. 169 2008 Exponential attractors for a nonlinear reaction-diffusion system in \(\mathbb R^3\). Zbl 1151.35315Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 111 2000 The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 96 2011 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113Miranville, Alain; Zelik, Sergey 84 2004 Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey 84 2004 Smooth attractors for strongly damped wave equations. Zbl 1113.35023Pata, Vittorino; Zelik, Sergey 78 2006 Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005Efendiev, M.; Zelik, S.; Miranville, A. 65 2005 The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Zbl 1041.35016Efendiev, M. A.; Zelik, S. V. 62 2001 Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020Miranville, A.; Zelik, S. 61 2005 Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053Kalantarov, Varga; Zelik, Sergey 53 2009 Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168Zelik, Sergey 50 2004 Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 44 2004 The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046Miranville, Alain; Zelik, Sergey 42 2010 A result on the existence of global attractors for semigroups of closed operators. Zbl 1152.47046Pata, Vittorino; Zelik, Sergey 40 2007 On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 39 2009 Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. Zbl 1133.35017Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino; Zelik, Sergey 33 2007 Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity. Zbl 1025.37044Zelik, Sergey V. 32 2003 A remark on the damped wave equation. Zbl 1140.35533Pata, Vittorino; Zelik, Sergey 32 2006 Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054Kalantarov, Varga K.; Zelik, Sergey 30 2012 Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey 29 2016 On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 29 2009 Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024Miranville, Alain; Zelik, Sergey 28 2002 On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 28 2014 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018Zelik, Sergey 27 2004 The attractor for a nonlinear hyperbolic equation in the unbounded domain. Zbl 1153.35311Zelik, S. V. 25 2001 Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 25 2010 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 23 2009 Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070Gatti, S.; Miranville, A.; Pata, V.; Zelik, S. 22 2008 Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V. 22 2011 Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067Zelik, Sergey 21 2007 Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027Efendiev, M.; Zelik, S. 21 2008 Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039Zelik, Sergey 20 2014 Strong trajectory attractor for a dissipative reaction-diffusion system. Zbl 1227.35084Vishik, M. I.; Zelik, S. V.; Chepyzhov, V. V. 19 2010 Existence and longtime behavior of a biofilm model. Zbl 1175.35017Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J. 19 2009 Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038Efendiev, M.; Zelik, S. 19 2002 Infinite energy solutions for damped Navier-Stokes equations in \({\mathbb{R}^2}\). Zbl 1293.35221Zelik, Sergey 19 2013 Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030Miranville, Alain; Pata, Vittorino; Zelik, Sergey 18 2007 The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov’s \(\varepsilon\)-entropy. Zbl 0989.35032Zelik, S. V. 17 2001 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 17 2014 On the strongly damped wave equation with memory. Zbl 1149.35015di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey 17 2008 Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain. Zbl 1258.35036Efendiev, M. A.; Zelik, S. V. 16 2002 Exponential attractors for random dynamical systems and applications. Zbl 1320.35089Shirikyan, Armen; Zelik, Sergey 16 2013 Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey 16 2010 Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations. Zbl 1178.34060Efendiev, M.; Zelik, S. 15 2009 Global and exponential attractors for 3-D wave equations with displacement dependent damping. Zbl 1101.35020Pata, Vittorino; Zelik, Sergey 15 2006 The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging. Zbl 1030.35016Efendiev, M.; Zelik, S. 15 2003 Attractors and their regularity for 2-D wave equations with nonlinear damping. Zbl 1145.35045Pata, Vittorino; Zelik, Sergey 15 2007 Global averaging and parametric resonances in damped semilinear wave equations. Zbl 1114.35131Zelik, S. 13 2006 Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185Savostianov, Anton; Zelik, Sergey 12 2014 Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056Kostianko, Anna; Zelik, Sergey 11 2015 Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 11 2003 A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366Gatti, Stefania; Pata, Vittorino; Zelik, Sergey 11 2009 Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081Eden, A.; Zelik, S. V.; Kalantarov, V. K. 11 2013 Regular attractors and nonautonomous perturbations of them. Zbl 1278.35027Vishik, Marko I.; Zelik, Sergey V.; Chepyzhov, Vladimir V. 11 2013 Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus. Zbl 1297.35010Bartuccelli, Michele; Deane, Jonathan; Zelik, Sergey 10 2013 Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045Efendiev, M.; Miranville, A.; Zelik, S. 10 2004 Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068Miranville, A.; Zelik, S. 9 2009 Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014Zelik, Sergey 9 2015 Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043Kostianko, Anna; Zelik, Sergey 8 2017 Multiparameter semigroups and attractors of reaction-diffusion equations in \(\mathbb R^n\). Zbl 1176.37025Zelik, S. V. 8 2004 Recent progress in attractors for quintic wave equations. Zbl 1349.35040Savostianov, Anton; Zelik, Sergey 8 2014 One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey 8 2016 Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains. Zbl 1125.35052Zelik, S. V. 8 2007 Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains. Zbl 1149.37328Efendiev, M.; Miranville, A.; Zelik, S. 7 2004 Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156Savostianov, Anton; Zelik, Sergey 7 2016 Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains. Zbl 1315.35039Eden, A.; Kalantarov, V. K.; Zelik, S. V. 7 2014 Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052Schimperna, Giulio; Zelik, Sergey 7 2013 Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in \(\mathbb R^3\). Zbl 1264.35055Zelik, Sergey; Pennant, Jon 6 2013 Regular attractor for a nonlinear elliptic system in a cylindrical domain. Zbl 0940.35085Vishik, M. I.; Zelik, S. V. 6 1999 Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129Zelik, Sergey 6 2008 Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 6 2012 Infinite-dimensional trajectory attractors of elliptic boundary value problems in cylindrical domains. Zbl 1049.37048Mielke, A.; Zelik, S. V. 6 2002 Infinite energy solutions for dissipative Euler equations in \(\mathbb{R}^2\). Zbl 1325.35137Chepyzhov, Vladimir; Zelik, Sergey 6 2015 Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Zbl 1133.35023Miranville, A.; Zelik, S. 5 2007 Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials. Zbl 1284.35085Eden, A.; Kalantarov, V. K.; Zelik, S. V. 5 2013 Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Zbl 1297.35164Anthony, Peter; Zelik, Sergey 5 2014 The finite dimensional attractor for a 4th order system of Cahn-Hilliard type with a supercritical nonlinearity. Zbl 1035.35019Efendiev, M. A.; Gajewski, H.; Zelik, S. 5 2002 Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033Kostianko, Anna; Zelik, Sergey 4 2018 An attractor of a nonlinear system of reaction-diffusion equations in \(\mathbb{R}^n\) and estimates of its \(\varepsilon\)-entropy. Zbl 0948.35016Zelik, S. V. 4 1999 Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in \(\mathbb R^3\). Zbl 1338.35064Savostianov, Anton; Zelik, Sergey 4 2016 Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051Zelik, S. V.; Ilyin, A. A. 4 2014 Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey 4 2019 Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\). Zbl 1327.35036Ilyin, Alexei; Patni, Kavita; Zelik, Sergey 4 2016 Analytical proof of space-time chaos in Ginzburg-Landau equations. Zbl 1213.35376Turaev, Dmitry; Zelik, Sergey 4 2010 Large dispersion, averaging and attractors: three 1D paradigms. Zbl 1406.35061Kostianko, Anna; Titi, Edriss; Zelik, Sergey 4 2018 On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 3 2016 The trajectory attractor of a nonlinear elliptic system in a cylindrical domain. Zbl 0871.35016Vishik, M. I.; Zelik, S. V. 3 1996 Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions. Zbl 1398.35145Chepyzhov, Vladimir; Ilyin, Alexei; Zelik, Sergey 3 2018 Strong trajectory and global \(\mathbf{W^{1,p}}\)-attractors for the damped-driven Euler system in \(\mathbb R^2\). Zbl 1359.35013Zelik, Sergey; Ilyin, Alexei; Chepyzhov, Vladimir 3 2017 A note on a strongly damped wave equation with fast growing nonlinearities. Zbl 1312.35134Kalantarov, Varga; Zelik, Sergey 3 2015 Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in \(\mathbb{R}^n\). Zbl 1125.35012Mielke, Alexander; Zelik, Sergey V. 3 2007 The attractor of a quasilinear hyperbolic equation with dissipation in \(\mathbb{R}^n\): Dimension and \(\varepsilon\)-entropy. Zbl 0974.35016Zelik, S. V. 2 2000 Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080Savostianov, Anton K.; Zelik, Sergeĭ V. 2 2020 Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey 2 2018 Formally gradient reaction-diffusion systems in \(\mathbb{R}^n\) have zero spatio-temporal topological entropy. Zbl 1058.35089Zelik, S. 2 2003 Classification of positive solutions of semilinear elliptic equations. Zbl 1048.35020Busca, Jérôme; Efendiev, Messoud; Zelik, S. 2 2004 Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations. Zbl 1308.35240Bridges, Thomas; Pennant, Jonathan; Zelik, Sergey 2 2014 Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Zbl 1304.35127Vishik, Mark I.; Zelik, Sergey 2 2014 Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101Ilyin, Alexei A.; Zelik, Sergey 2 2021 Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential. Zbl 1184.35070Segatti, Antonio; Zelik, Sergey 1 2009 Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101Ilyin, Alexei A.; Zelik, Sergey 2 2021 Validity of the hyperbolic Whitham modulation equations in Sobolev spaces. Zbl 1455.35233Bridges, Thomas J.; Kostianko, Anna; Zelik, Sergey 1 2021 Infinite energy solutions for weakly damped quintic wave equations in \(\mathbb{R}^3\). Zbl 1460.35040Mei, Xinyu; Savostianov, Anton; Sun, Chunyou; Zelik, Sergey 1 2021 Sharp dimension estimates for the attractors of the regularized damped Euler system. Zbl 1477.35149Zelik, S. V.; Ilyin, A. A.; Kostianko, A. G. 1 2021 Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080Savostianov, Anton K.; Zelik, Sergeĭ V. 2 2020 Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196Ilyin, Alexei; Laptev, Ari; Zelik, Sergey 1 2020 Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey 4 2019 On the Lieb-Thirring constant on the torus. Zbl 1436.35268Zelik, S. V.; Ilyin, A. A.; Laptev, A. A. 1 2019 Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033Kostianko, Anna; Zelik, Sergey 4 2018 Large dispersion, averaging and attractors: three 1D paradigms. Zbl 1406.35061Kostianko, Anna; Titi, Edriss; Zelik, Sergey 4 2018 Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions. Zbl 1398.35145Chepyzhov, Vladimir; Ilyin, Alexei; Zelik, Sergey 3 2018 Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey 2 2018 Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043Kostianko, Anna; Zelik, Sergey 8 2017 Strong trajectory and global \(\mathbf{W^{1,p}}\)-attractors for the damped-driven Euler system in \(\mathbb R^2\). Zbl 1359.35013Zelik, Sergey; Ilyin, Alexei; Chepyzhov, Vladimir 3 2017 Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey 29 2016 One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey 8 2016 Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156Savostianov, Anton; Zelik, Sergey 7 2016 Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in \(\mathbb R^3\). Zbl 1338.35064Savostianov, Anton; Zelik, Sergey 4 2016 Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\). Zbl 1327.35036Ilyin, Alexei; Patni, Kavita; Zelik, Sergey 4 2016 On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 3 2016 Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056Kostianko, Anna; Zelik, Sergey 11 2015 Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014Zelik, Sergey 9 2015 Infinite energy solutions for dissipative Euler equations in \(\mathbb{R}^2\). Zbl 1325.35137Chepyzhov, Vladimir; Zelik, Sergey 6 2015 A note on a strongly damped wave equation with fast growing nonlinearities. Zbl 1312.35134Kalantarov, Varga; Zelik, Sergey 3 2015 On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 28 2014 Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039Zelik, Sergey 20 2014 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 17 2014 Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185Savostianov, Anton; Zelik, Sergey 12 2014 Recent progress in attractors for quintic wave equations. Zbl 1349.35040Savostianov, Anton; Zelik, Sergey 8 2014 Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains. Zbl 1315.35039Eden, A.; Kalantarov, V. K.; Zelik, S. V. 7 2014 Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Zbl 1297.35164Anthony, Peter; Zelik, Sergey 5 2014 Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051Zelik, S. V.; Ilyin, A. A. 4 2014 Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations. Zbl 1308.35240Bridges, Thomas; Pennant, Jonathan; Zelik, Sergey 2 2014 Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Zbl 1304.35127Vishik, Mark I.; Zelik, Sergey 2 2014 Regular attractors of autonomous and nonautonomous dynamical systems. Zbl 1307.37012Zelik, S. V.; Chepyzhov, V. V. 1 2014 Infinite energy solutions for damped Navier-Stokes equations in \({\mathbb{R}^2}\). Zbl 1293.35221Zelik, Sergey 19 2013 Exponential attractors for random dynamical systems and applications. Zbl 1320.35089Shirikyan, Armen; Zelik, Sergey 16 2013 Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081Eden, A.; Zelik, S. V.; Kalantarov, V. K. 11 2013 Regular attractors and nonautonomous perturbations of them. Zbl 1278.35027Vishik, Marko I.; Zelik, Sergey V.; Chepyzhov, Vladimir V. 11 2013 Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus. Zbl 1297.35010Bartuccelli, Michele; Deane, Jonathan; Zelik, Sergey 10 2013 Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052Schimperna, Giulio; Zelik, Sergey 7 2013 Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in \(\mathbb R^3\). Zbl 1264.35055Zelik, Sergey; Pennant, Jon 6 2013 Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials. Zbl 1284.35085Eden, A.; Kalantarov, V. K.; Zelik, S. V. 5 2013 Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054Kalantarov, Varga K.; Zelik, Sergey 30 2012 Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 6 2012 The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 96 2011 Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V. 22 2011 The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046Miranville, Alain; Zelik, Sergey 42 2010 Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 25 2010 Strong trajectory attractor for a dissipative reaction-diffusion system. Zbl 1227.35084Vishik, M. I.; Zelik, S. V.; Chepyzhov, V. V. 19 2010 Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey 16 2010 Analytical proof of space-time chaos in Ginzburg-Landau equations. Zbl 1213.35376Turaev, Dmitry; Zelik, Sergey 4 2010 Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053Kalantarov, Varga; Zelik, Sergey 53 2009 On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 39 2009 On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 29 2009 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 23 2009 Existence and longtime behavior of a biofilm model. Zbl 1175.35017Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J. 19 2009 Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations. Zbl 1178.34060Efendiev, M.; Zelik, S. 15 2009 A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366Gatti, Stefania; Pata, Vittorino; Zelik, Sergey 11 2009 Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068Miranville, A.; Zelik, S. 9 2009 Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential. Zbl 1184.35070Segatti, Antonio; Zelik, Sergey 1 2009 Attractors for dissipative partial differential equations in bounded and unbounded domains. Zbl 1221.37158Miranville, A.; Zelik, S. 169 2008 Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070Gatti, S.; Miranville, A.; Pata, V.; Zelik, S. 22 2008 Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027Efendiev, M.; Zelik, S. 21 2008 On the strongly damped wave equation with memory. Zbl 1149.35015di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey 17 2008 Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129Zelik, Sergey 6 2008 A result on the existence of global attractors for semigroups of closed operators. Zbl 1152.47046Pata, Vittorino; Zelik, Sergey 40 2007 Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials. Zbl 1133.35017Grasselli, Maurizio; Miranville, Alain; Pata, Vittorino; Zelik, Sergey 33 2007 Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067Zelik, Sergey 21 2007 Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030Miranville, Alain; Pata, Vittorino; Zelik, Sergey 18 2007 Attractors and their regularity for 2-D wave equations with nonlinear damping. Zbl 1145.35045Pata, Vittorino; Zelik, Sergey 15 2007 Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains. Zbl 1125.35052Zelik, S. V. 8 2007 Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Zbl 1133.35023Miranville, A.; Zelik, S. 5 2007 Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in \(\mathbb{R}^n\). Zbl 1125.35012Mielke, Alexander; Zelik, Sergey V. 3 2007 Smooth attractors for strongly damped wave equations. Zbl 1113.35023Pata, Vittorino; Zelik, Sergey 78 2006 A remark on the damped wave equation. Zbl 1140.35533Pata, Vittorino; Zelik, Sergey 32 2006 Global and exponential attractors for 3-D wave equations with displacement dependent damping. Zbl 1101.35020Pata, Vittorino; Zelik, Sergey 15 2006 Global averaging and parametric resonances in damped semilinear wave equations. Zbl 1114.35131Zelik, S. 13 2006 Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005Efendiev, M.; Zelik, S.; Miranville, A. 65 2005 Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020Miranville, A.; Zelik, S. 61 2005 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113Miranville, Alain; Zelik, Sergey 84 2004 Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey 84 2004 Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168Zelik, Sergey 50 2004 Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 44 2004 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018Zelik, Sergey 27 2004 Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045Efendiev, M.; Miranville, A.; Zelik, S. 10 2004 Multiparameter semigroups and attractors of reaction-diffusion equations in \(\mathbb R^n\). Zbl 1176.37025Zelik, S. V. 8 2004 Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains. Zbl 1149.37328Efendiev, M.; Miranville, A.; Zelik, S. 7 2004 Classification of positive solutions of semilinear elliptic equations. Zbl 1048.35020Busca, Jérôme; Efendiev, Messoud; Zelik, S. 2 2004 The long-time behaviour of the thermoconvective flow in a porous medium. Zbl 1156.37323Efendiev, M. A.; Fuhrmann, J.; Zelik, S. V. 1 2004 Dynamical approach for positive solutions of semilinear elliptic problems in unbounded domains. Zbl 1107.35349Berestycki, H.; Efendiev, M.; Zelik, S. 1 2004 Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity. Zbl 1025.37044Zelik, Sergey V. 32 2003 The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging. Zbl 1030.35016Efendiev, M.; Zelik, S. 15 2003 Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 11 2003 Formally gradient reaction-diffusion systems in \(\mathbb{R}^n\) have zero spatio-temporal topological entropy. Zbl 1058.35089Zelik, S. 2 2003 Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024Miranville, Alain; Zelik, Sergey 28 2002 Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038Efendiev, M.; Zelik, S. 19 2002 Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain. Zbl 1258.35036Efendiev, M. A.; Zelik, S. V. 16 2002 Infinite-dimensional trajectory attractors of elliptic boundary value problems in cylindrical domains. Zbl 1049.37048Mielke, A.; Zelik, S. V. 6 2002 The finite dimensional attractor for a 4th order system of Cahn-Hilliard type with a supercritical nonlinearity. Zbl 1035.35019Efendiev, M. A.; Gajewski, H.; Zelik, S. 5 2002 ...and 9 more Documents all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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Second Series ...and 111 more Serials all top 5 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) Citations by Year