Edit Profile 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: 120 Publications since 1994, including 1 Book Reviewing Activity: 84 Reviews all top 5 Co-Authors 23 single-authored 21 Miranville, Alain M. 17 Efendiev, Messoud 11 Pata, Vittorino 10 Ilyin, Alexei A. 8 Chepyzhov, Vladimir V. 8 Kalantarov, Varga K. 6 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 1 Anthony, Peter 1 Bartuccelli, Michele V. 1 Berestycki, Henri 1 Bilgin, Bilgesu A. 1 Busca, Jérôme 1 Deane, Jonathan H. B. 1 di Plinio, Francesco 1 Eberl, Hermann J. 1 Fuhrmann, Jürgen 1 Gajewski, Herbert 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 Sun, Chunyou 1 Titi, Edriss Saleh 1 Warner, Christopher all top 5 Serials 12 Communications on Pure and Applied Analysis 7 Mathematical Methods in the Applied Sciences 7 Mathematical Notes 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 Discrete and Continuous Dynamical Systems. Series B 3 Asymptotic Analysis 3 Journal of Dynamics and Differential Equations 3 Sbornik: Mathematics 3 Doklady 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 Physica D 2 Advances in Differential Equations 2 Journal of Evolution Equations 1 Archive for Rational Mechanics and Analysis 1 Rocky Mountain Journal of Mathematics 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 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 115 Partial differential equations (35-XX) 44 Dynamical systems and ergodic theory (37-XX) 8 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 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-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 103 Publications have been cited 1,835 times in 890 Documents Cited by ▼ Year ▼ Attractors for dissipative partial differential equations in bounded and unbounded domains. Zbl 1221.37158Miranville, A.; Zelik, S. 142 2008 Exponential attractors for a nonlinear reaction-diffusion system in \(\mathbb R^3\). Zbl 1151.35315Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 98 2000 Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey 82 2004 The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 79 2011 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113Miranville, Alain; Zelik, Sergey 70 2004 Smooth attractors for strongly damped wave equations. Zbl 1113.35023Pata, Vittorino; Zelik, Sergey 62 2006 Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005Efendiev, M.; Zelik, S.; Miranville, A. 60 2005 The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Zbl 1041.35016Efendiev, M. A.; Zelik, S. V. 59 2001 Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020Miranville, A.; Zelik, S. 54 2005 Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168Zelik, Sergey 45 2004 Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053Kalantarov, Varga; Zelik, Sergey 44 2009 A result on the existence of global attractors for semigroups of closed operators. Zbl 1152.47046Pata, Vittorino; Zelik, Sergey 39 2007 Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 39 2004 The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046Miranville, Alain; Zelik, Sergey 35 2010 On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 34 2009 Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity. Zbl 1025.37044Zelik, Sergey V. 32 2003 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 30 2007 A remark on the damped wave equation. Zbl 1140.35533Pata, Vittorino; Zelik, Sergey 28 2006 Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024Miranville, Alain; Zelik, Sergey 27 2002 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018Zelik, Sergey 26 2004 Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey 25 2016 The attractor for a nonlinear hyperbolic equation in the unbounded domain. Zbl 1153.35311Zelik, S. V. 25 2001 On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 25 2009 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 23 2009 Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054Kalantarov, Varga K.; Zelik, Sergey 22 2012 Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 20 2010 Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067Zelik, Sergey 20 2007 Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027Efendiev, M.; Zelik, S. 19 2008 Strong trajectory attractor for a dissipative reaction-diffusion system. Zbl 1227.35084Vishik, M. I.; Zelik, S. V.; Chepyzhov, V. V. 19 2010 Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070Gatti, S.; Miranville, A.; Pata, V.; Zelik, S. 19 2008 On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 18 2014 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 Infinite energy solutions for damped Navier-Stokes equations in \({\mathbb{R}^2}\). Zbl 1293.35221Zelik, Sergey 17 2013 Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V. 17 2011 Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038Efendiev, M.; Zelik, S. 16 2002 Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030Miranville, Alain; Pata, Vittorino; Zelik, Sergey 16 2007 On the strongly damped wave equation with memory. Zbl 1149.35015di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey 16 2008 Existence and longtime behavior of a biofilm model. Zbl 1175.35017Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J. 16 2009 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 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 Attractors and their regularity for 2-D wave equations with nonlinear damping. Zbl 1145.35045Pata, Vittorino; Zelik, Sergey 15 2007 Global and exponential attractors for 3-D wave equations with displacement dependent damping. Zbl 1101.35020Pata, Vittorino; Zelik, Sergey 15 2006 Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039Zelik, Sergey 14 2014 Exponential attractors for random dynamical systems and applications. Zbl 1320.35089Shirikyan, Armen; Zelik, Sergey 14 2013 Global averaging and parametric resonances in damped semilinear wave equations. Zbl 1114.35131Zelik, S. 12 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. 12 2003 Regular attractors and nonautonomous perturbations of them. Zbl 1278.35027Vishik, Marko I.; Zelik, Sergey V.; Chepyzhov, Vladimir V. 11 2013 Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 10 2003 Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185Savostianov, Anton; Zelik, Sergey 9 2014 Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045Efendiev, M.; Miranville, A.; Zelik, S. 9 2004 A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366Gatti, Stefania; Pata, Vittorino; Zelik, Sergey 9 2009 Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081Eden, A.; Zelik, S. V.; Kalantarov, V. K. 9 2013 Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068Miranville, A.; Zelik, S. 8 2009 Recent progress in attractors for quintic wave equations. Zbl 1349.35040Savostianov, Anton; Zelik, Sergey 8 2014 Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains. Zbl 1125.35052Zelik, S. V. 8 2007 One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey 8 2016 Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus. Zbl 1297.35010Bartuccelli, Michele; Deane, Jonathan; Zelik, Sergey 8 2013 Multiparameter semigroups and attractors of reaction-diffusion equations in \(\mathbb R^n\). Zbl 1176.37025Zelik, S. V. 7 2004 Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056Kostianko, Anna; Zelik, Sergey 7 2015 Global and exponential attractors for nonlinear reaction-diffusion systems in unbounded domains. Zbl 1149.37328Efendiev, M.; Miranville, A.; Zelik, S. 7 2004 Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014Zelik, Sergey 7 2015 Infinite energy solutions for dissipative Euler equations in \(\mathbb{R}^2\). Zbl 1325.35137Chepyzhov, Vladimir; Zelik, Sergey 6 2015 Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129Zelik, Sergey 6 2008 Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains. Zbl 1315.35039Eden, A.; Kalantarov, V. K.; Zelik, S. V. 6 2014 Regular attractor for a nonlinear elliptic system in a cylindrical domain. Zbl 0940.35085Vishik, M. I.; Zelik, S. V. 6 1999 Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156Savostianov, Anton; Zelik, Sergey 6 2016 Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in \(\mathbb R^3\). Zbl 1264.35055Zelik, Sergey; Pennant, Jon 6 2013 Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 6 2012 Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043Kostianko, Anna; Zelik, Sergey 5 2017 Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Zbl 1133.35023Miranville, A.; Zelik, S. 5 2007 Infinite-dimensional trajectory attractors of elliptic boundary value problems in cylindrical domains. Zbl 1049.37048Mielke, A.; Zelik, S. V. 5 2002 Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Zbl 1297.35164Anthony, Peter; Zelik, Sergey 5 2014 Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052Schimperna, Giulio; Zelik, Sergey 5 2013 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 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 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. 4 2002 Analytical proof of space-time chaos in Ginzburg-Landau equations. Zbl 1213.35376Turaev, Dmitry; Zelik, Sergey 4 2010 Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials. Zbl 1284.35085Eden, A.; Kalantarov, V. K.; Zelik, S. V. 4 2013 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 Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051Zelik, S. V.; Ilyin, A. A. 3 2014 The trajectory attractor of a nonlinear elliptic system in a cylindrical domain. Zbl 0871.35016Vishik, M. I.; Zelik, S. V. 3 1996 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 On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 3 2016 Classification of positive solutions of semilinear elliptic equations. Zbl 1048.35020Busca, Jérôme; Efendiev, Messoud; Zelik, S. 2 2004 Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033Kostianko, Anna; Zelik, Sergey 2 2018 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 The attractor of a quasilinear hyperbolic equation with dissipation in \(\mathbb{R}^n\): Dimension and \(\varepsilon\)-entropy. Zbl 0974.35016Zelik, S. V. 2 2000 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 the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey 2 2019 Formally gradient reaction-diffusion systems in \(\mathbb{R}^n\) have zero spatio-temporal topological entropy. Zbl 1058.35089Zelik, S. 2 2003 Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in \(\mathbb R^3\). Zbl 1338.35064Savostianov, Anton; Zelik, Sergey 2 2016 Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Zbl 1304.35127Vishik, Mark I.; Zelik, Sergey 2 2014 On the Lieb-Thirring constant on the torus. Zbl 1436.35268Zelik, S. V.; Ilyin, A. A.; Laptev, A. A. 1 2019 Regular attractors of autonomous and nonautonomous dynamical systems. Zbl 1307.37012Zelik, S. V.; Chepyzhov, V. V. 1 2014 Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080Savostianov, Anton K.; Zelik, Sergeĭ V. 1 2020 A note on a strongly damped wave equation with fast growing nonlinearities. Zbl 1312.35134Kalantarov, Varga; Zelik, Sergey 1 2015 Dynamical approach for positive solutions of semilinear elliptic problems in unbounded domains. Zbl 1107.35349Berestycki, H.; Efendiev, M.; Zelik, S. 1 2004 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 1 2018 Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080Savostianov, Anton K.; Zelik, Sergeĭ V. 1 2020 Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey 2 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 2 2018 Hyperbolic relaxation of the 2D Navier-Stokes equations in a bounded domain. Zbl 1398.35147Ilyin, Alexei; Rykov, Yuri; Zelik, Sergey 2 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 1 2018 Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043Kostianko, Anna; Zelik, Sergey 5 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 25 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 6 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 Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in \(\mathbb R^3\). Zbl 1338.35064Savostianov, Anton; Zelik, Sergey 2 2016 Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056Kostianko, Anna; Zelik, Sergey 7 2015 Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014Zelik, Sergey 7 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 1 2015 On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 18 2014 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 17 2014 Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039Zelik, Sergey 14 2014 Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185Savostianov, Anton; Zelik, Sergey 9 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. 6 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. 3 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 17 2013 Exponential attractors for random dynamical systems and applications. Zbl 1320.35089Shirikyan, Armen; Zelik, Sergey 14 2013 Regular attractors and nonautonomous perturbations of them. Zbl 1278.35027Vishik, Marko I.; Zelik, Sergey V.; Chepyzhov, Vladimir V. 11 2013 Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081Eden, A.; Zelik, S. V.; Kalantarov, V. K. 9 2013 Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus. Zbl 1297.35010Bartuccelli, Michele; Deane, Jonathan; Zelik, Sergey 8 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 Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052Schimperna, Giulio; Zelik, Sergey 5 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. 4 2013 Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054Kalantarov, Varga K.; Zelik, Sergey 22 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 79 2011 Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V. 17 2011 The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046Miranville, Alain; Zelik, Sergey 35 2010 Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 20 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 44 2009 On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 34 2009 On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 25 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. 16 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 9 2009 Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068Miranville, A.; Zelik, S. 8 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. 142 2008 Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027Efendiev, M.; Zelik, S. 19 2008 Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070Gatti, S.; Miranville, A.; Pata, V.; Zelik, S. 19 2008 On the strongly damped wave equation with memory. Zbl 1149.35015di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey 16 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 39 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 30 2007 Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067Zelik, Sergey 20 2007 Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030Miranville, Alain; Pata, Vittorino; Zelik, Sergey 16 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 62 2006 A remark on the damped wave equation. Zbl 1140.35533Pata, Vittorino; Zelik, Sergey 28 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. 12 2006 Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005Efendiev, M.; Zelik, S.; Miranville, A. 60 2005 Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020Miranville, A.; Zelik, S. 54 2005 Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey 82 2004 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113Miranville, Alain; Zelik, Sergey 70 2004 Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168Zelik, Sergey 45 2004 Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 39 2004 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018Zelik, Sergey 26 2004 Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045Efendiev, M.; Miranville, A.; Zelik, S. 9 2004 Multiparameter semigroups and attractors of reaction-diffusion equations in \(\mathbb R^n\). Zbl 1176.37025Zelik, S. V. 7 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 Dynamical approach for positive solutions of semilinear elliptic problems in unbounded domains. Zbl 1107.35349Berestycki, H.; Efendiev, M.; Zelik, S. 1 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 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. 12 2003 Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 10 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 27 2002 Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038Efendiev, M.; Zelik, S. 16 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. 5 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. 4 2002 The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Zbl 1041.35016Efendiev, M. A.; Zelik, S. V. 59 2001 The attractor for a nonlinear hyperbolic equation in the unbounded domain. Zbl 1153.35311Zelik, S. V. 25 2001 The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov’s \(\varepsilon\)-entropy. Zbl 0989.35032Zelik, S. V. 17 2001 The dynamics of fast non-autonomous travelling waves and homogenization. Zbl 1004.35010Zelik, S. 1 2001 Exponential attractors for a nonlinear reaction-diffusion system in \(\mathbb R^3\). Zbl 1151.35315Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 98 2000 The attractor of a quasilinear hyperbolic equation with dissipation in \(\mathbb{R}^n\): Dimension and \(\varepsilon\)-entropy. Zbl 0974.35016Zelik, S. V. 2 2000 ...and 3 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 782 Authors 72 Miranville, Alain M. 52 Zelik, Sergey V. 36 Grasselli, Maurizio 31 Zhong, Chengkui 29 Pata, Vittorino 26 Gal, Ciprian Gheorghe Sorin 24 Yang, Zhijian 23 Zhou, Shengfan 21 Conti, Monica C. 20 Chepyzhov, Vladimir V. 20 Sun, Chunyou 19 Schimperna, Giulio 18 Colli, Pierluigi 18 Gatti, Stefania 17 Efendiev, Messoud 15 Wu, Hao 14 Cherfils, Laurence 12 Cholewa, Jan W. 12 Gilardi, Gianni 12 Ilyin, Alexei A. 12 Rocca, Elisabetta 11 Kalantarov, Varga K. 11 Kasyanov, Pavlo O. 11 Scarpa, Luca 10 Giorgini, Andrea 10 Meng, Fengjuan 10 Nolasco de Carvalho, Alexandre 10 Quintanilla de Latorre, Ramón 10 Shomberg, Joseph L. 10 Yang, Meihua 9 Eberl, Hermann J. 9 Kloeden, Peter Eris 9 Ma, To Fu 9 Rodríguez-Bernal, Aníbal 9 Sonner, Stefanie 9 Sprekels, Jürgen 9 Yang, Lu 8 Khanmamedov, Azer Kh. 8 Laptev, Ari 8 Valero, José 8 Vishik, Marko Iosifovich 8 Zhao, Caidi 7 Bonfoh, Ahmed S. 7 Caraballo Garrido, Tomás 7 Chueshov, Igor’ Dmitrievich 7 Fakih, Hussein 7 Gorban, Nataliia V. 7 Langa, Jose’ Antonio 7 Lasiecka, Irena 7 Li, Xiaojun 7 Liu, Zhiming 7 Marchini, Elsa Maria 7 Pražák, Dalibor 7 Segatti, Antonio 7 Webster, Justin T. 7 Xie, Yongqin 7 You, Bo 7 Yue, Gaocheng 6 Ding, Pengyan 6 Dlotko, Tomasz W. 6 Geredeli, Pelin G. 6 Kostianko, Anna 6 Liu, Cuncai 6 Pierre, Morgan 6 Robinson, James Cooper 6 Rossi, Riccarda 6 Wang, Zhaojuan 6 Zhang, Jin 5 Coti Zelati, Michele 5 Cui, Hongyong 5 Czaja, Radosław 5 Frigeri, Sergio 5 Gallay, Thierry 5 Ghasemi, Maryam 5 Goubet, Olivier 5 Li, Ke 5 Marín-Rubio, Pedro 5 Niu, Weisheng 5 Petzeltová, Hana 5 Qin, Yuming 5 Slijepčević, Siniša 5 Wang, Yonghai 5 Yang, Xinguang 5 Zhao, Xiaopeng 5 Zhu, Kaixuan 4 Arrieta, José M. 4 Bessaih, Hakima 4 Cavaterra, Cecilia 4 Chechkin, Gregory Aleksandrovich 4 Davoli, Elisa 4 Dell’Oro, Filippo 4 Duan, Jinqiao 4 Feng, Na 4 Fukao, Takeshi 4 Guo, Yanqiu 4 Ju, Xuewei 4 Kapustyan, Oleksiy V. 4 Knees, Dorothee 4 Lam, Kei Fong 4 Li, Desheng ...and 682 more Authors all top 5 Cited in 192 Serials 64 Journal of Differential Equations 59 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 58 Journal of Mathematical Analysis and Applications 38 Discrete and Continuous Dynamical Systems. Series B 37 Communications on Pure and Applied Analysis 32 Discrete and Continuous Dynamical Systems 21 Mathematical Methods in the Applied Sciences 21 Nonlinear Analysis. Real World Applications 19 Journal of Mathematical Physics 18 Journal of Dynamics and Differential Equations 15 Applicable Analysis 15 Applied Mathematics and Optimization 15 Physica D 15 Applied Mathematics Letters 13 Journal of Evolution Equations 12 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 11 Applied Mathematics and Computation 10 Nonlinearity 10 Quarterly of Applied Mathematics 10 SIAM Journal on Mathematical Analysis 10 Journal of Nonlinear Science 9 Evolution Equations and Control Theory 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Journal of Applied Analysis and Computation 7 Archive for Rational Mechanics and Analysis 7 Computers & Mathematics with Applications 7 Applications of Mathematics 7 Journal of Mathematical Fluid Mechanics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 Journal of Computational and Applied Mathematics 6 Asymptotic Analysis 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Acta Mathematica Sinica. English Series 5 Mathematical Notes 5 Chaos, Solitons and Fractals 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Transactions of the American Mathematical Society 5 Journal of Scientific Computing 5 Russian Journal of Mathematical Physics 5 NoDEA. Nonlinear Differential Equations and Applications 5 Discrete Dynamics in Nature and Society 5 Central European Journal of Mathematics 5 Discrete and Continuous Dynamical Systems. Series S 4 Communications in Mathematical Physics 4 Russian Mathematical Surveys 4 Acta Applicandae Mathematicae 4 European Journal of Applied Mathematics 4 Calculus of Variations and Partial Differential Equations 4 Doklady Mathematics 4 Abstract and Applied Analysis 4 Mediterranean Journal of Mathematics 4 Boundary Value Problems 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 Communications in Partial Differential Equations 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Topological Methods in Nonlinear Analysis 3 Electronic Journal of Differential Equations (EJDE) 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 Stochastics and Dynamics 3 Milan Journal of Mathematics 3 Advances in Difference Equations 3 Complex Variables and Elliptic Equations 3 Mathematical Control and Related Fields 3 Journal of Elliptic and Parabolic Equations 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 Studies in Applied Mathematics 2 Chinese Annals of Mathematics. Series B 2 Stochastic Analysis and Applications 2 Applied Numerical Mathematics 2 Set-Valued Analysis 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 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Multiscale Modeling & Simulation 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 SIAM Journal on Imaging Sciences 2 Set-Valued and Variational Analysis 2 Science China. Mathematics 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 ISRN Mathematical Analysis 2 Stochastic and Partial Differential Equations. Analysis and Computations 2 Open Mathematics ...and 92 more Serials all top 5 Cited in 34 Fields 804 Partial differential equations (35-XX) 257 Dynamical systems and ergodic theory (37-XX) 127 Fluid mechanics (76-XX) 77 Mechanics of deformable solids (74-XX) 64 Classical thermodynamics, heat transfer (80-XX) 48 Numerical analysis (65-XX) 39 Ordinary differential equations (34-XX) 39 Operator theory (47-XX) 39 Biology and other natural sciences (92-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 33 Probability theory and stochastic processes (60-XX) 30 Integral equations (45-XX) 30 Statistical mechanics, structure of matter (82-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Systems theory; control (93-XX) 8 Real functions (26-XX) 8 Computer science (68-XX) 6 Measure and integration (28-XX) 6 Functional analysis (46-XX) 5 Quantum theory (81-XX) 4 Mechanics of particles and systems (70-XX) 3 Difference and functional equations (39-XX) 3 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 General topology (54-XX) 2 Algebraic topology (55-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Manifolds and cell complexes (57-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year