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.; Zelik, Serguei more...less Homepage: http://sergey-zelik.co.uk/ External Links: MGP · ORCID · Math-Net.Ru · dblp Documents Indexed: 135 Publications since 1994, including 1 Book 1 Further Contribution Reviewing Activity: 84 Reviews Co-Authors: 49 Co-Authors with 110 Joint Publications 1,401 Co-Co-Authors all top 5 Co-Authors 23 single-authored 21 Miranville, Alain M. 17 Efendiev, Messoud 16 Ilyin, Alexei A. 14 Kostianko, Anna 11 Kalantarov, Varga K. 11 Pata, Vittorino 8 Chepyzhov, Vladimir V. 6 Schimperna, Giulio 6 Vishik, Marko Iosifovich 5 Laptev, Ari 4 Grasselli, Maurizio 4 Mielke, Alexander 4 Segatti, Antonio 3 Eden, Alp 3 Galusinski, Cédric 3 Gatti, Stefania 3 Sun, Chunyou 3 Turaev, Dmitry V. 2 Bridges, Thomas J. 2 Cherfils, Laurence 2 Deane, Jonathan H. B. 2 Fabrie, Pierre 1 Anthony, Peter 1 Bartuccelli, Michele V. 1 Berestycki, Henri 1 Bevan, Jonathan J. 1 Bilgin, Bilgesu Arif 1 Busca, Jérôme 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 Ladyzhenskaya, Ol’ga Aleksandrovna 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 Seregin, Gregory A. 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 8 Discrete and Continuous Dynamical Systems 7 Mathematical Methods in the Applied Sciences 6 Nonlinearity 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Russian Mathematical Surveys 4 Mathematische Nachrichten 4 Journal of Dynamics and Differential Equations 4 Doklady Mathematics 4 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Differential Equations 3 Physica D 3 Asymptotic Analysis 3 Sbornik: Mathematics 3 Journal of Mathematical Fluid Mechanics 2 Communications on Pure and Applied Mathematics 2 Journal of Mathematical Physics 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 Mathematische Annalen 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 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 Turkish Journal of Mathematics 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 Discrete and Continuous Dynamical Systems. Series S 1 Bulletin of Mathematical Sciences 1 Stochastic and Partial Differential Equations. Analysis and Computations 1 Cambridge Mathematical Library all top 5 Fields 130 Partial differential equations (35-XX) 47 Dynamical systems and ergodic theory (37-XX) 13 Fluid mechanics (76-XX) 6 Real functions (26-XX) 5 Ordinary differential equations (34-XX) 5 Mechanics of deformable solids (74-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Operator theory (47-XX) 3 Measure and integration (28-XX) 2 Integral equations (45-XX) 2 Functional analysis (46-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-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 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 113 Publications have been cited 2,337 times in 1,159 Documents Cited by ▼ Year ▼ Attractors for dissipative partial differential equations in bounded and unbounded domains. Zbl 1221.37158Miranville, A.; Zelik, S. 182 2008 Exponential attractors for a nonlinear reaction-diffusion system in \(\mathbb R^3\). Zbl 1151.35315Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 113 2000 The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 106 2011 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113Miranville, Alain; Zelik, Sergey 93 2004 Smooth attractors for strongly damped wave equations. Zbl 1113.35023Pata, Vittorino; Zelik, Sergey 89 2006 Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey 86 2004 Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005Efendiev, M.; Zelik, S.; Miranville, A. 68 2005 Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020Miranville, A.; Zelik, S. 67 2005 The attractor for a nonlinear reaction-diffusion system in an unbounded domain. Zbl 1041.35016Efendiev, M. A.; Zelik, S. V. 65 2001 Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053Kalantarov, Varga; Zelik, Sergey 60 2009 Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168Zelik, Sergey 59 2004 Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 47 2004 The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046Miranville, Alain; Zelik, Sergey 46 2010 Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054Kalantarov, Varga K.; Zelik, Sergey 44 2012 On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 42 2009 A result on the existence of global attractors for semigroups of closed operators. Zbl 1152.47046Pata, Vittorino; Zelik, Sergey 40 2007 A remark on the damped wave equation. Zbl 1140.35533Pata, Vittorino; Zelik, Sergey 38 2006 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 34 2007 Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity. Zbl 1025.37044Zelik, Sergey V. 34 2003 Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey 34 2016 On a generalized Cahn-Hilliard equation with biological applications. Zbl 1304.35133Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 33 2014 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018Zelik, Sergey 31 2004 On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 31 2009 Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024Miranville, Alain; Zelik, Sergey 29 2002 Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039Zelik, Sergey 28 2014 Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070Gatti, S.; Miranville, A.; Pata, V.; Zelik, S. 27 2008 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 27 2009 The attractor for a nonlinear hyperbolic equation in the unbounded domain. Zbl 1153.35311Zelik, S. V. 27 2001 Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 26 2010 Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067Zelik, Sergey 24 2007 Existence and longtime behavior of a biofilm model. Zbl 1175.35017Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J. 23 2009 Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V. 23 2011 Infinite energy solutions for damped Navier-Stokes equations in \({\mathbb{R}^2}\). Zbl 1293.35221Zelik, Sergey 23 2013 Finite- and infinite-dimensional attractors for porous media equations. Zbl 1132.37027Efendiev, M.; Zelik, S. 21 2008 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 21 2014 Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization. Zbl 1036.35038Efendiev, M.; Zelik, S. 20 2002 The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov’s \(\varepsilon\)-entropy. Zbl 0989.35032Zelik, S. V. 20 2001 On the strongly damped wave equation with memory. Zbl 1149.35015di Plinio, Francesco; Pata, Vittorino; Zelik, Sergey 20 2008 Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030Miranville, Alain; Pata, Vittorino; Zelik, Sergey 19 2007 Strong trajectory attractor for a dissipative reaction-diffusion system. Zbl 1227.35084Vishik, M. I.; Zelik, S. V.; Chepyzhov, V. V. 19 2010 Exponential attractors for random dynamical systems and applications. Zbl 1320.35089Shirikyan, Armen; Zelik, Sergey 19 2013 Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations. Zbl 1178.34060Efendiev, M.; Zelik, S. 17 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. 17 2002 The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging. Zbl 1030.35016Efendiev, M.; Zelik, S. 16 2003 Continuous families of exponential attractors for singularly perturbed equations with memory. Zbl 1196.35054Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey 16 2010 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 for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions. Zbl 1372.35043Kostianko, Anna; Zelik, Sergey 15 2017 Global averaging and parametric resonances in damped semilinear wave equations. Zbl 1114.35131Zelik, S. 14 2006 Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056Kostianko, Anna; Zelik, Sergey 14 2015 Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014Zelik, Sergey 14 2015 A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366Gatti, Stefania; Pata, Vittorino; Zelik, Sergey 13 2009 Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081Eden, A.; Zelik, S. V.; Kalantarov, V. K. 13 2013 Smooth attractors for the quintic wave equations with fractional damping. Zbl 1352.37185Savostianov, Anton; Zelik, Sergey 12 2014 Infinite dimensional exponential attractors for a non-autonomous reaction-diffusion system. Zbl 1025.37043Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 11 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 nonlinear reaction-diffusion systems in unbounded domains and their approximation. Zbl 1072.35045Efendiev, M.; Miranville, A.; Zelik, S. 10 2004 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 Doubly nonlinear Cahn-Hilliard-Gurtin equations. Zbl 1191.35068Miranville, A.; Zelik, S. 9 2009 Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033Kostianko, Anna; Zelik, Sergey 9 2018 Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations. Zbl 1278.35052Schimperna, Giulio; Zelik, Sergey 9 2013 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. 8 2004 Recent progress in attractors for quintic wave equations. Zbl 1349.35040Savostianov, Anton; Zelik, Sergey 8 2014 Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156Savostianov, Anton; Zelik, Sergey 8 2016 Infinite energy solutions for dissipative Euler equations in \(\mathbb{R}^2\). Zbl 1325.35137Chepyzhov, Vladimir; Zelik, Sergey 8 2015 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 Large dispersion, averaging and attractors: three 1D paradigms. Zbl 1406.35061Kostianko, Anna; Titi, Edriss; Zelik, Sergey 8 2018 Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129Zelik, Sergey 8 2008 Infinite-dimensional trajectory attractors of elliptic boundary value problems in cylindrical domains. Zbl 1049.37048Mielke, A.; Zelik, S. V. 7 2002 Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 7 2012 Infinite-energy solutions for the Cahn-Hilliard equation in cylindrical domains. Zbl 1315.35039Eden, A.; Kalantarov, V. K.; Zelik, S. V. 7 2014 Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey 6 2019 Regular attractor for a nonlinear elliptic system in a cylindrical domain. Zbl 0940.35085Vishik, M. I.; Zelik, S. V. 6 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. 6 2002 Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\). Zbl 1327.35036Ilyin, Alexei; Patni, Kavita; Zelik, Sergey 6 2016 Infinite-energy solutions for the Navier-Stokes equations in a strip revisited. Zbl 1297.35164Anthony, Peter; Zelik, Sergey 6 2014 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. 6 2013 Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type. Zbl 1133.35023Miranville, A.; Zelik, S. 5 2007 Analytical proof of space-time chaos in Ginzburg-Landau equations. Zbl 1213.35376Turaev, Dmitry; Zelik, Sergey 5 2010 Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in \(\mathbb R^3\). Zbl 1338.35064Savostianov, Anton; Zelik, Sergey 5 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 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 4 2017 Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101Ilyin, Alexei A.; Zelik, Sergey 4 2021 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 4 2018 On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 4 2016 Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051Zelik, S. V.; Ilyin, A. A. 4 2014 On the Lieb-Thirring constant on the torus. Zbl 1436.35268Zelik, S. V.; Ilyin, A. A.; Laptev, A. A. 3 2019 Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080Savostianov, Anton K.; Zelik, Sergeĭ V. 3 2020 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 trajectory attractor of a nonlinear elliptic system in a cylindrical domain. Zbl 0871.35016Vishik, M. I.; Zelik, S. V. 3 1996 Formally gradient reaction-diffusion systems in \(\mathbb{R}^n\) have zero spatio-temporal topological entropy. Zbl 1058.35089Zelik, S. 3 2003 A note on a strongly damped wave equation with fast growing nonlinearities. Zbl 1312.35134Kalantarov, Varga; Zelik, Sergey 3 2015 Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196Ilyin, Alexei; Laptev, Ari; Zelik, Sergey 3 2020 The attractor of a quasilinear hyperbolic equation with dissipation in \(\mathbb{R}^n\): Dimension and \(\varepsilon\)-entropy. Zbl 0974.35016Zelik, S. V. 2 2000 Classification of positive solutions of semilinear elliptic equations. Zbl 1048.35020Busca, Jérôme; Efendiev, Messoud; Zelik, S. 2 2004 Infinite energy solutions for weakly damped quintic wave equations in \(\mathbb{R}^3\). Zbl 1460.35040Mei, Xinyu; Savostianov, Anton; Sun, Chunyou; Zelik, Sergey 2 2021 Sharp dimension estimates for the attractors of the regularized damped Euler system. Zbl 1477.35149Zelik, S. V.; Ilyin, A. A.; Kostianko, A. G. 2 2021 Determining functionals and finite-dimensional reduction for dissipative PDEs revisited. Zbl 1504.35071Kalantarov, Varga; Kostianko, Anna; Zelik, Sergey 1 2023 Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations. Zbl 1490.35273Ilyin, Alexei; Kostianko, Anna; Zelik, Sergey 1 2022 Estimates for the dimension of attractors of a regularized Euler system with dissipation on the sphere. Zbl 07488478Zelik, S. V.; Ilyin, A. A.; Kostyanko, A. G. 1 2022 Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations. Zbl 1479.35101Ilyin, Alexei A.; Zelik, Sergey 4 2021 Infinite energy solutions for weakly damped quintic wave equations in \(\mathbb{R}^3\). Zbl 1460.35040Mei, Xinyu; Savostianov, Anton; Sun, Chunyou; Zelik, Sergey 2 2021 Sharp dimension estimates for the attractors of the regularized damped Euler system. Zbl 1477.35149Zelik, S. V.; Ilyin, A. A.; Kostianko, A. G. 2 2021 Validity of the hyperbolic Whitham modulation equations in Sobolev spaces. Zbl 1455.35233Bridges, Thomas J.; Kostianko, Anna; Zelik, Sergey 1 2021 Asymptotic regularity and attractors for slightly compressible Brinkman-Forchheimer equations. Zbl 1479.35671Kalantarov, Varga; Zelik, Sergey 1 2021 Uniform attractors for measure-driven quintic wave equations. Zbl 1445.35080Savostianov, Anton K.; Zelik, Sergeĭ V. 3 2020 Lieb-Thirring constant on the sphere and on the torus. Zbl 1450.35196Ilyin, Alexei; Laptev, Ari; Zelik, Sergey 3 2020 Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Zbl 1411.35173Chepyzhov, Vladimir V.; Kostianko, Anna; Zelik, Sergey 6 2019 On the Lieb-Thirring constant on the torus. Zbl 1436.35268Zelik, S. V.; Ilyin, A. A.; Laptev, A. A. 3 2019 Inertial manifolds for 1D reaction-diffusion-advection systems. II: Periodic boundary conditions. Zbl 1377.35033Kostianko, Anna; Zelik, Sergey 9 2018 Large dispersion, averaging and attractors: three 1D paradigms. Zbl 1406.35061Kostianko, Anna; Titi, Edriss; Zelik, Sergey 8 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 4 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 15 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 4 2017 Attractors for damped quintic wave equations in bounded domains. Zbl 1356.35055Kalantarov, Varga; Savostianov, Anton; Zelik, Sergey 34 2016 Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space. Zbl 1381.35156Savostianov, Anton; Zelik, Sergey 8 2016 One-dimensional interpolation inequalities, Carlson-Landau inequalities, and magnetic Schrödinger operators. Zbl 1336.35016Ilyin, Alexei; Laptev, Ari; Loss, Michael; Zelik, Sergey 8 2016 Upper bounds for the attractor dimension of damped Navier-Stokes equations in \(\mathbb R^2\). Zbl 1327.35036Ilyin, Alexei; Patni, Kavita; Zelik, Sergey 6 2016 Finite dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono equation in \(\mathbb R^3\). Zbl 1338.35064Savostianov, Anton; Zelik, Sergey 5 2016 On a singular heat equation with dynamic boundary conditions. Zbl 1344.35146Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 4 2016 Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions. Zbl 1331.35056Kostianko, Anna; Zelik, Sergey 14 2015 Strong uniform attractors for non-autonomous dissipative PDEs with non translation-compact external forces. Zbl 1335.35014Zelik, Sergey 14 2015 Infinite energy solutions for dissipative Euler equations in \(\mathbb{R}^2\). Zbl 1325.35137Chepyzhov, Vladimir; Zelik, Sergey 8 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 33 2014 Inertial manifolds and finite-dimensional reduction for dissipative PDEs. Zbl 1343.35039Zelik, Sergey 28 2014 On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms. Zbl 1295.35036Mielke, Alexander; Zelik, Sergey 21 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 6 2014 Green’s function asymptotics and sharp interpolation inequalities. Zbl 1314.46051Zelik, S. V.; Ilyin, A. A. 4 2014 Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Zbl 1304.35127Vishik, Mark I.; Zelik, Sergey 2 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 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 23 2013 Exponential attractors for random dynamical systems and applications. Zbl 1320.35089Shirikyan, Armen; Zelik, Sergey 19 2013 Counterexamples to regularity of Mañé projections in the theory of attractors. Zbl 1282.35081Eden, A.; Zelik, S. V.; Kalantarov, V. K. 13 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 9 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. 6 2013 Smooth attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities. Zbl 1264.35054Kalantarov, Varga K.; Zelik, Sergey 44 2012 Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model. Zbl 1270.35151Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 7 2012 The Cahn-Hilliard equation with logarithmic potentials. Zbl 1250.35129Cherfils, Laurence; Miranville, Alain; Zelik, Sergey 106 2011 Strong trajectory attractors for dissipative Euler equations. Zbl 1230.35092Chepyzhov, V. V.; Vishik, M. I.; Zelik, S. V. 23 2011 The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. Zbl 1203.35046Miranville, Alain; Zelik, Sergey 46 2010 Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term. Zbl 1198.35038Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 26 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 5 2010 Finite-dimensional attractors for the quasi-linear strongly-damped wave equation. Zbl 1183.35053Kalantarov, Varga; Zelik, Sergey 60 2009 On the 2D Cahn-Hilliard equation with inertial term. Zbl 1173.35086Grasselli, Maurizio; Schimperna, Giulio; Zelik, Sergey 42 2009 On the 3D Cahn-Hilliard equation with inertial term. Zbl 1239.35160Grasselli, Maurizio; Schimperna, Giulio; Segatti, Antonio; Zelik, Sergey 31 2009 Multi-pulse evolution and space-time chaos in dissipative systems. Zbl 1163.37003Zelik, Sergey; Mielke, Alexander 27 2009 Existence and longtime behavior of a biofilm model. Zbl 1175.35017Efendiev, Messoud A.; Zelik, Sergey; Eberl, Hermann J. 23 2009 Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations. Zbl 1178.34060Efendiev, M.; Zelik, S. 17 2009 A Gronwall-type Lemma with parameter and dissipative estimates for PDEs. Zbl 1167.34366Gatti, Stefania; Pata, Vittorino; Zelik, Sergey 13 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. 182 2008 Attractors for semi-linear equations of viscoelasticity with very low dissipation. Zbl 1179.35070Gatti, S.; Miranville, A.; Pata, V.; Zelik, S. 27 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 20 2008 Weak spatially nondecaying solutions of 3D, Navier-Stokes equations in cylindrical domains. Zbl 1296.35129Zelik, Sergey 8 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 34 2007 Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip. Zbl 1142.35067Zelik, Sergey 24 2007 Exponential attractors for singularly perturbed damped wave equations: a simple construction. Zbl 1139.35030Miranville, Alain; Pata, Vittorino; Zelik, Sergey 19 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 89 2006 A remark on the damped wave equation. Zbl 1140.35533Pata, Vittorino; Zelik, Sergey 38 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. 14 2006 Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems. Zbl 1088.37005Efendiev, M.; Zelik, S.; Miranville, A. 68 2005 Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions. Zbl 1068.35020Miranville, A.; Zelik, S. 67 2005 Robust exponential attractors for Cahn-Hilliard type equations with singular potentials. Zbl 1050.35113Miranville, Alain; Zelik, Sergey 93 2004 Uniform exponential attractors for a singularly perturbed damped wave equation. Zbl 1060.35011Fabrie, Pierre; Galusinski, Cedric; Miranville, Alain; Zelik, Sergey 86 2004 Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Zbl 1197.35168Zelik, Sergey 59 2004 Exponential attractors for a singularly perturbed Cahn-Hilliard system. Zbl 1046.37047Efendiev, Messoud; Miranville, Alain; Zelik, Sergey 47 2004 Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities. Zbl 1059.35018Zelik, Sergey 31 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. 8 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. 34 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. 16 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. 3 2003 Robust exponential attractors for singularly perturbed phase-field type equations. Zbl 1004.35024Miranville, Alain; Zelik, Sergey 29 2002 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,024 Authors 82 Miranville, Alain M. 63 Zelik, Sergey V. 38 Grasselli, Maurizio 38 Zhong, Chengkui 31 Pata, Vittorino 30 Yang, Zhijian 27 Gal, Ciprian Gheorghe Sorin 25 Sun, Chunyou 24 Colli, Pierluigi 24 Zhou, Shengfan 22 Chepyzhov, Vladimir V. 22 Conti, Monica C. 22 Schimperna, Giulio 20 Efendiev, Messoud 20 Wu, Hao 18 Gatti, Stefania 17 Ilyin, Alexei A. 16 Cherfils, Laurence 15 Gilardi, Gianni 14 Kalantarov, Varga K. 14 Rocca, Elisabetta 14 Scarpa, Luca 13 Caraballo Garrido, Tomás 13 Cholewa, Jan W. 13 Eberl, Hermann J. 13 Kostianko, Anna 13 Meng, Fengjuan 13 Mohan, Manil Thankamani 12 Giorgini, Andrea 12 Shomberg, Joseph L. 12 Sonner, Stefanie 12 Xie, Yongqin 12 Yang, Lu 11 Kasyanov, Pavlo O. 11 Kloeden, Peter Eris 11 Nolasco de Carvalho, Alexandre 11 Sprekels, Jürgen 10 Bonfoh, Ahmed S. 10 Quintanilla de Latorre, Ramón 10 Yang, Meihua 9 Khanmamedov, Azer Kh. 9 Langa, Jose’ Antonio 9 Ma, To Fu 9 Qin, Yuming 9 Rodríguez-Bernal, Aníbal 9 Vishik, Marko Iosifovich 9 You, Bo 9 Zhao, Caidi 9 Zhu, Kaixuan 8 Cui, Hongyong 8 Fakih, Hussein 8 Gorban, Nataliia V. 8 Laptev, Ari 8 Lasiecka, Irena 8 Liu, Cuncai 8 Liu, Zhiming 8 Nguyen Huy Tuan 8 Pierre, Morgan 8 Robinson, James Cooper 8 Valero, José 8 Webster, Justin T. 8 Zhao, Xiaopeng 7 Chueshov, Igor’ Dmitrievich 7 Ding, Pengyan 7 Fukao, Takeshi 7 Lam, Kei Fong 7 Li, Xiaojun 7 Li, Yanan 7 Li, Yangrong 7 Makki, Ahmad 7 Marchini, Elsa Maria 7 Pražák, Dalibor 7 Rossi, Riccarda 7 Segatti, Antonio 7 Wang, Cheng 7 Wang, Yonghai 7 Yue, Gaocheng 7 Zhang, Jin 6 Czaja, Radosław 6 Dell’Oro, Filippo 6 Dlotko, Tomasz W. 6 Geredeli, Pelin Guven 6 Ghasemi, Maryam 6 Goubet, Olivier 6 Knees, Dorothee 6 Ma, Qiaozhen 6 Maniar, Lahcen 6 Mei, Xinyu 6 Niu, Weisheng 6 Slijepčević, Siniša 6 Titi, Edriss Saleh 6 Wang, Zhaojuan 6 Wise, Steven M. 6 Yang, Xinguang 6 Zhao, Chunxiang 5 Bezerra, Flank David Morais 5 Chechkin, Gregory Aleksandrovich 5 Coti Zelati, Michele 5 Feng, Na 5 Frigeri, Sergio ...and 924 more Authors all top 5 Cited in 232 Serials 75 Journal of Differential Equations 66 Journal of Mathematical Analysis and Applications 61 Nonlinear Analysis. 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