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Professor Sergey Zelik


Programme Leader
+44 (0)1483 682636
27 AA 04

Biography

Research interests

Details can be found on my personal web page.

My publications

Publications

Bridges Thomas J, Kostianko Anna, Zelik Sergey (2021)Validity of the hyperbolic Whitham modulation equations in Sobolev spaces, In: Journal of Differential Equations274pp. 971-995 Elsevier Inc
Grasselli M, Miranville A, Zelik S (2009)Preface, In: Discrete and Continuous Dynamical Systems - Series S2(1)
Chepyzhov VV, Vishik MI, Zelik Sergey (2011)Strong trajectory attractors for dissipative Euler equations, In: Journal des Mathematiques Pures et Appliquees96pp. 395-407 Elsevier Masson
Kalantarov V, Zelik S (2009)Finite-dimensional attractors for the quasi-linear strongly-damped wave equation, In: JOURNAL OF DIFFERENTIAL EQUATIONS247(4)pp. 1120-1155 ACADEMIC PRESS INC ELSEVIER SCIENCE
Efendiev M, Zelik S (2009)Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations, In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES32(13)pp. 1638-1668 JOHN WILEY & SONS LTD
Cherfils L, Miranville A, Zelik S (2011)The Cahn-Hilliard Equation with Logarithmic Potentials, In: Milan Journal of Mathematics79(2)pp. 561-596 Springer
Miranville A, Zelik S (2009)Doubly nonlinear Cahn-Hilliard-Gurtin equations, In: HOKKAIDO MATHEMATICAL JOURNAL38(2)pp. 315-360
Turaev D, Zelik S (2003)Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations, In: NONLINEARITY16(6)PII S0951-pp. 2163-2198 IOP PUBLISHING LTD
Fabrie P, Galusinski C, Miranville A, Zelik S (2004)Uniform exponential attractors for a singularly perturbed damped wave equation, In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS10(1-2)pp. 211-238 AMER INST MATHEMATICAL SCIENCES
Turaev D, Vladimirov AG, Zelik S (2007)Chaotic bound state of localized structures in the complex Ginzburg-Landau equation, In: PHYSICAL REVIEW E75(4)ARTN 0pp. ?-? AMERICAN PHYSICAL SOC
Vishik MI, Zelik SV (1996)The trajectory attractor of a non-linear elliptic system in a cylindrical domain, In: SBORNIK MATHEMATICS187(11-12)pp. 1755-1789 LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES
Efendiev M, Miranville A, Zelik S (2004)Global and exponential attractors for nonlinear react ion-diffusion systems in unbounded domains, In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS134pp. 271-315 ROYAL SOC EDINBURGH
Zelik S (2008)On the Lyapunov dimension of cascade systems, In: COMMUN PUR APPL ANAL7(4)pp. 971-985 AMER INST MATHEMATICAL SCIENCES
Vishik MI, Zelik SV (1999)Regular attractor for a non-linear elliptic system in a cylindrical domain, In: SBORNIK MATHEMATICS190(5-6)pp. 803-834 LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES
Zelik SV, Chepyzhov VV (2014)Regular attractors of autonomous and nonautonomous dynamical systems, In: DOKLADY MATHEMATICS89(1)pp. 92-97 MAIK NAUKA/INTERPERIODICA/SPRINGER
Efendiev MA, Fuhrmann J, Zelik SV (2004)The long-time behaviour of the thermoconvective flow in a porous medium, In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES27(8)pp. 907-930 JOHN WILEY & SONS LTD
Miranville A, Zelik S (2004)Robust exponential attractors for Cahn-Hilliard type equations with singular potentials, In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES27(5)pp. 545-582 JOHN WILEY & SONS LTD
Efendiev M, Miranville A, Zelik S (2004)Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation, In: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES460(2044)pp. 1107-1129 ROYAL SOC
Turaev DV, Warner C, Zelik S (2014)Energy growth for a nonlinear oscillator coupled to a monochromatic wave, In: REGULAR & CHAOTIC DYNAMICS19(4)pp. 513-522 MAIK NAUKA/INTERPERIODICA/SPRINGER
Zelik SV (2003)Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity, In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS56(5)pp. 584-637 JOHN WILEY & SONS INC
Zelik SV, Ilyin AA (2014)Green's function asymptotics and sharp interpolation inequalities, In: Russian Mathematical Surveys69(2)pp. 209-260
Gatti S, Miranville A, Pata V, Zelik S (2008)Attractors for semi-linear equations of viscoelasticity with very low dissipation, In: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS38(4)pp. 1117-1138 ROCKY MT MATH CONSORTIUM
Kalantarov V, Savostianov A, Zelik S (2013)Attractors for damped quintic wave equations in bounded domains
Gatti S, Pata V, Zelik S (2009)A Gronwall-type lemma with parameter and dissipative estimates for PDEs, In: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS70(6)pp. 2337-2343 PERGAMON-ELSEVIER SCIENCE LTD
Efendiev M, Miranville A, Zelik S (2003)Infinite dimensional exponential attractors for a non-autonomous react ion-diffusion system, In: MATHEMATISCHE NACHRICHTEN248pp. 72-96 WILEY-V C H VERLAG GMBH
Savostianov A, Zelik S (2014)Smooth attractors for the quintic wave equations with fractional damping, In: ASYMPTOTIC ANALYSIS87(3-4)pp. 191-221 IOS PRESS
Vishik MI, Chepyzhov VV, Zelik SV (2013)Regular attractors and nonautonomous perturbations of them, In: Sbornik Mathematics204(1)pp. 1-42
Zelik SV (1998)A trajectory attractor of a nonlinear elliptic system in an unbounded domain, In: MATHEMATICAL NOTES63(1-2)pp. 120-123 PLENUM PUBL CORP
Efendiev M, Miranville A, Zelik S (2004)Exponential attractors for a singularly perturbed Cahn-Hilliard system, In: MATHEMATISCHE NACHRICHTEN272pp. 11-31 WILEY-V C H VERLAG GMBH
Di Plinio F, Pata V, Zelik S (2008)On the strongly damped wave equation with memory, In: INDIANA UNIVERSITY MATHEMATICS JOURNAL57pp. 757-780
Zelik S (2015)STRONG UNIFORM ATTRACTORS FOR NON-AUTONOMOUS DISSIPATIVE PDES WITH NON TRANSLATION-COMPACT EXTERNAL FORCES, In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B20(3)pp. 781-810 AMER INST MATHEMATICAL SCIENCES
Grasselli M, Miranville A, Pata V, Zelik S (2007)Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials, In: MATHEMATISCHE NACHRICHTEN280(13-14)pp. 1475-1509 WILEY-V C H VERLAG GMBH
Efendiev M, Zelik S (2008)Finite- and infinite-dimensional attractors for porous media equations, In: PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY96pp. 51-77 LONDON MATH SOC
Anthony P, Zelik S (2014)Infinite-energy solutions for the Navier-Stokes equations in a strip revisited, In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS13(4)pp. 1361-1393 AMER INST MATHEMATICAL SCIENCES
Kostianko A, Zelik S (2015)Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions., In: Communications on Pure and Applied Analysis14(5)pp. 2069-2094 AMER INST MATHEMATICAL SCIENCES
Pata V, Zelik S (2006)A remark on the damped wave equation, In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS5(3)pp. 609-614 AMER INST MATHEMATICAL SCIENCES
Ilyin A, Laptev A, Loss M, Zelik S (2015)One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrodinger operators, In: International Mathematics Research Notices Oxford University Press
Savostianov A, Zelik S (2015)Finite Dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono Equation in R3, In: Mathematical Methods in the Applied Sciences39(5)pp. 1254-1267
Miranville A, Zelik S (2010)THE CAHN-HILLIARD EQUATION WITH SINGULAR POTENTIALS AND DYNAMIC BOUNDARY CONDITIONS, In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS28(1)pp. 275-310 AMER INST MATHEMATICAL SCIENCES
Eden A, Kalantarov VK, Zelik Sergey (2010)Infinite energy solutions for the Cahn-Hilliard equation in cylindrical domains, In: arXiv
Gatti S, Miranville A, Pata V, Zelik S (2010)Continuous families of exponential attractors for singularly perturbed equations with memory, In: P ROY SOC EDINB A140pp. 329-366 ROYAL SOC EDINBURGH
Kostianko Anna, Titi Edriss, Zelik Sergey (2018)Large dispersion, averaging and attractors: three 1D paradigms, In: Nonlinearity31(12)R317 IOP Publishing
Shirikyan A, Zelik S (2012)Exponential attractors for random dynamical systems and applications, In: Stochastic Partial Differential Equations: Analysis and Computations1(2)pp. 241-281 Springer
Mielke A, Zelik S (2014)On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms, In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE13(1)pp. 67-135 SCUOLA NORMALE SUPERIORE
Vladimirov AG, Turaev D, Zelik S (2011)Synchronization of interacting temporal cavity oscillons, In: Proceedings of Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference
Chepyzhov V, Zelik S (2015)Infinite Energy Solutions for Dissipative Euler Equations in R-2, In: Journal of Mathematical Fluid Mechanics17(3)pp. 513-532 SPRINGER BASEL AG
Efendiev M, Zelik S (2003)The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging, In: Advances in Differential Equations8(6)pp. 673-732
Vishik MI, Zelik SV, Chepyzhov VV (2010)Strong Trajectory Attractor for a Dissipative Reaction-Diffusion System, In: DOKLADY MATHEMATICS82(3)pp. 869-873 MAIK NAUKA/INTERPERIODICA/SPRINGER
Efendiev M, Zelik S (2002)Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization, In: ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE19(6)pp. 961-989 GAUTHIER-VILLARS/EDITIONS ELSEVIER
Bilgen B, Kalantarov V, Zelik S (2015)Preventing blow up by convective terms in dissipative PDEs., In: arXiv
Ilyin A, Patni K, Zelik S (2016)Upper bounds for the attractor dimension of damped Navier-Stokes equations in R 2, In: Discrete and Continuous Dynamical Systems - Series A36(4)pp. 2085-2102 American Insitute of Mathematical Sciences
Grasselli M, Schimperna G, Zelik S (2009)On the 2D Cahn-Hilliard Equation with Inertial Term, In: Communications in Partial Differential Equations34(2)PII 909499pp. 137-170 Taylor & Francis
Ilyin A, Laptev A, Zelik S (2015)Sharp interpolation inequalities for discrete operators and applications, In: BULLETIN OF MATHEMATICAL SCIENCES5(1)pp. 19-57 Springer
Zelik S (2014)Inertial manifolds and finite-dimensional reduction for dissipative PDEs, In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics144(6)pp. 1245-1327 CAMBRIDGE UNIV PRESS
Efendiev MA, Gajewski H, Zelik S (2002)The finite dimensional attractor for a 4th order system of cahn-hilliard type with a supercritical nonlinearity, In: Advances in Differential Equations7(9)pp. 1073-1100
Kalantarov V, Zelik S (2015)A note on a strongly damped wave equation with fast growing nonlinearities, In: JOURNAL OF MATHEMATICAL PHYSICS56(1)ARTN 0pp. ?-? AMER INST PHYSICS
Grasselli M, Schimperna G, Zelik S (2010)Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term, In: NONLINEARITY23(3)pp. 707-737 IOP PUBLISHING LTD
Kostianko A, Titi E, Zelik S (2016)Large dispersion, averaging and attractors: three 1D paradigms, In: arXiv
Miranville A, Zelik S (2002)Robust exponential attractors for singularly perturbed phase-field type equations, In: Electronic Journal of Differential Equations2002
Efendiev MA, Zelik SV (2002)Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain, In: Journal of Dynamics and Differential Equations14(2)pp. 369-403
Mielke A, Zelik SV (2002)Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains, In: RUSSIAN MATHEMATICAL SURVEYS57(4)pp. 753-784 LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES
Turaev D, Vladimirov AG, Zelik S (2009)Strong enhancement of interaction of optical pulses induced by oscillatory instability, In: Proceedings of European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference IEEE
Efendiev M, Miranville A, Zelik S (2000)Exponential attractors for a nonlinear reaction-diffusion system in R-3, In: COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE330(8)pp. 713-718 EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
Turaev D, Vladimirov AG, Zelik S (2012)Long-Range Interaction and Synchronization of Oscillating Dissipative Solitons, In: PHYSICAL REVIEW LETTERS108(26)ARTN 2pp. ?-? AMER PHYSICAL SOC
Pata V, Zelik S (2006)Smooth attractors for strongly damped wave equations, In: NONLINEARITY19(7)pp. 1495-1506 IOP PUBLISHING LTD
Bridges Thomas, Pennant J, Zelik Sergey (2014)Degenerate Hyperbolic Conservation Laws with Dissipation: Reduction to and Validity of a Class of Burgers-Type Equations, In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS214(2)pp. 671-716 SPRINGER
Zelik SV (2001)The attractor for a nonlinear hyperbolic equation in the unbounded domain, In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS7(3)pp. 593-641 SOUTHWEST MISSOURI STATE UNIV
Zelik SV (1997)Boundedness of the solutions of a nonlinear elliptic system in a cylindrical domain, In: MATHEMATICAL NOTES61(3-4)pp. 365-369 PLENUM PUBL CORP
Mielke A, Zelik SV (2007)Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in R-n, In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS19(2)pp. 333-389 SPRINGER
Zelik S, Pata V (2006)Global and exponential attractors for 3-D wave equations with displacement dependent damping, In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES29(11)pp. 1291-1306 JOHN WILEY & SONS LTD
ZELIK SV (1994)ALMOST-PERIODIC SOLUTIONS OF A CLASS OF LINEAR HYPERBOLIC-EQUATIONS, In: MATHEMATICAL NOTES56(1-2)pp. 865-868 PLENUM PUBL CORP
Zelik S, Pennant J (2013)GLOBAL WELL-POSEDNESS IN UNIFORMLY LOCAL SPACES FOR THE CAHN-HILLIARD EQUATION IN R-3, In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS12(1)pp. 461-480 AMER INST MATHEMATICAL SCIENCES
Miranville A, Zelik S (2008)Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains, In: Handbook of Differential Equations: Evolutionary Equations4pp. 103-200
Ilyin A, Laptev A, Zelik S (2015)Sharp interpolation inequalities for discrete operators and applications, In: BULLETIN OF MATHEMATICAL SCIENCES5(1)pp. 19-57 SPRINGER BASEL AG
Schimperna G, Segatti A, Zelik S (2012)Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model, In: Journal of Evolution Equations12(4)pp. 863-890
Efendiev MA, Zelik SV (2001)The attractor for a nonlinear reaction-diffusion system in an unbounded domain, In: Communications on Pure and Applied Mathematics54(6)
Cherfils L, Miranville A, Zelik S (2014)ON A GENERALIZED CAHN-HILLIARD EQUATION WITH BIOLOGICAL APPLICATIONS, In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B19(7)pp. 2013-2026 AMER INST MATHEMATICAL SCIENCES
Zelik S, Mielke A (2009)Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems, In: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY198(925)pp. VI-95 AMER MATHEMATICAL SOC
Efendiev M, Zelik S, Miranville A (2005)Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems, In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS135pp. 703-730 ROYAL SOC EDINBURGH
Rossides T, Lloyd David, Zelik S (2015)Computing Interacting Multi-fronts in One Dimensional Real Ginzburg Landau Equations, In: JOURNAL OF SCIENTIFIC COMPUTING63(3)pp. 799-819 SPRINGER/PLENUM PUBLISHERS
Zelik S (2004)Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities, In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS11(2-3)pp. 351-392 AMER INST MATHEMATICAL SCIENCES
Turaev D, Zelik S, Vladimirov AG (2005)Chaotic bound state of localized structures in the complex ginzburg-landau equation, In: Optics InfoBase Conference Papers
Miranville A, Zelik S (2005)Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions, In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES28(6)pp. 709-735 JOHN WILEY & SONS LTD
Miranville A, Pata V, Zelik S (2007)Exponential attractors for singularly perturbed damped wave equations: A simple construction, In: ASYMPTOTIC ANALYSIS53(1-2)pp. 1-12 IOS PRESS
Zelik S (2004)Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent, In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS3(4)pp. 921-934 AMER INST MATHEMATICAL SCIENCES
Zelik S (2006)Global averaging and parametric resonances in damped semilinear wave equations, In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS136pp. 1053-1097 ROYAL SOC EDINBURGH
Zelik SV, Ilyin AA, Laptev AA (2015)Sharp interpolation inequalities for discrete operators, In: DOKLADY MATHEMATICS91(2)pp. 215-219 MAIK NAUKA/INTERPERIODICA/SPRINGER
Zelik S (2007)Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip, In: GLASGOW MATHEMATICAL JOURNAL49pp. 525-588 CAMBRIDGE UNIV PRESS
Miranville A, Zelik S (2007)Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type, In: NONLINEARITY20(8)pp. 1773-1797 IOP PUBLISHING LTD
Zelik SV (2007)Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains, In: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS19(1)pp. 1-74 SPRINGER
Busca J, Efendiev M, Zelik S (2004)Classification of positive solutions of semilinear elliptic equations, In: COMPTES RENDUS MATHEMATIQUE338(1)pp. 7-11 EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
Efendiev MA, Zelik SV, Eberl HJ (2009)Existence and longtime behavior of a biofilm model, In: Communications on Pure and Applied Analysis8(2)pp. 509-531 American Institute of Mathematical Sciences
Grasselli M, Schimperna G, Segatti A, Zelik S (2009)On the 3D Cahn-Hilliard equation with inertial term, In: JOURNAL OF EVOLUTION EQUATIONS9(2)pp. 371-404 BIRKHAUSER VERLAG AG
Pata V, Zelik S (2007)A result on the existence of global attractors for semigroups of closed operators, In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS6(2)pp. 481-486 AMER INST MATHEMATICAL SCIENCES