Exponential attractors for random dynamical systems and applications
The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE’s. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction–diffus...
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| Published in | Stochastic partial differential equations : analysis and computations Vol. 1; no. 2; pp. 241 - 281 |
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| Format | Journal Article |
| Language | English |
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| Abstract | The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE’s. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction–diffusion system with a random perturbation. We show, in particular, that the attractors can be constructed in such a way that the symmetric distance between the attractors for stochastic and deterministic problems goes to zero with the amplitude of the random perturbation. |
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| AbstractList | The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE’s. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then apply these results to a nonlinear reaction–diffusion system with a random perturbation. We show, in particular, that the attractors can be constructed in such a way that the symmetric distance between the attractors for stochastic and deterministic problems goes to zero with the amplitude of the random perturbation. |
| Author | Shirikyan, Armen Zelik, Sergey |
| Author_xml | – sequence: 1 givenname: Armen surname: Shirikyan fullname: Shirikyan, Armen email: Armen.Shirikyan@u-cergy.fr organization: Department of Mathematics, University of Cergy-Pontoise – sequence: 2 givenname: Sergey surname: Zelik fullname: Zelik, Sergey organization: Department of Mathematics, University of Surrey |
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| Keywords | Reaction-diffusion equation 35R60 Random exponential attractors 35B41 35K57 60H15 Stochastic PDE’s |
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| References | TemamRInfinite-Dimensional Dynamical Systems in Mechanics and Physics1988New YorkSpringer0662.3500110.1007/978-1-4684-0313-8 CrauelHDebusscheAFlandoliFRandom attractorsJ. Dyn. Differ. Equ.19979230734114512940884.5806410.1007/BF02219225 Miranville, A., Zelik, S.: Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains. Handbook of Differential Equations: Evolutionary Equations, vol. IV, pp. 103–200. North-Holland, Amsterdam (2008) EfendievMMiranvilleAZelikSExponential attractors for a nonlinear reaction–diffusion system in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}^3$$\end{document}C. R. Acad. Sci. Paris I2000330871371817639161151.3531510.1016/S0764-4442(00)00259-7 StroockDProbability. An Analytic Viewpoint1993CambridgeCambridge University Press ChueshovIScheutzowMSchmalfussBContinuity properties of inertial manifolds for stochastic retarded semilinear parabolic equations. Interacting Stochastic Systems2005BerlinSpringer BensoussanAFlandoliFStochastic inertial manifoldStoch. Stoch. Rep.1995531–2133913804880854.60059 EfendievMMiranvilleAZelikSInfinite dimensional exponential attractors for a non-autonomous reaction-diffusion systemMath. Nachr.2003248/2497296195071610.1002/mana.200310004 CrauelHFlandoliFAttractors for random dynamical systemsProbab. Theory Relat. Fields1994100336539313055870819.5802310.1007/BF01193705 HallPHeydeCCMartingale Limit Theory and Its Application1980New YorkAcademic Press0462.60045 Chepyzhov, V.V., Vishik, M.I.: Attractors for Equations of Mathematical Physics, vol. 49. AMS, Providence (2002) Chepyzhov, V., Vishik, M., Zelik, S.: Regular attractors and their non-autonomous perturbations. Mat. Sb. (N.S.) (2012) (to appear) FoiasCSellGTemamRInertial manifolds for nonlinear evolutionary equationsJ. Differ. Equ.19887323093539439450643.5800410.1016/0022-0396(88)90110-6 BabinAVVishikMIAttractors of Evolution Equations1992AmsterdamNorth-Holland Publishing0778.58002 ChepyzhovVGoritskyAGlobal integral manifolds with exponential tracking for nonautonomous equationsRuss. J. Math. Phys.19975192814867600908.34044 ChueshovIScheutzowMOn the structure of attractors and invariant measures for a class of monotone random systemsDyn. Syst.200419212714420604221061.3703210.1080/1468936042000207792 Kunita, H.: Stochastic Flows and Stochastic Differential Equations. Cambridge University Press, Cambridge (1997) KaratzasIShreveSEBrownian Motion and Stochastic Calculus1991New YorkSpringer0734.60060 CarvalhoALangaJRobinsonJAttractors for Infinite-Dimensional Non-Autonomous Dynamical Systems2013New YorkSpringer1263.3700210.1007/978-1-4614-4581-4 FabriePGalusinskiCMiranvilleAZelikSUniform exponential attractors for a singularly perturbed damped wave equationDiscret. Contin. Dyn. Syst.2004101–221123820261921060.35011 ArnoldLRandom Dynamical Systems1998BerlinSpringer0906.3400110.1007/978-3-662-12878-7 Walters, P.: An Introduction to Ergodic Theory. Graduate Texts in Mathematics, vol. 79. Springer, New York (1982) LangaJMiranvilleARealJPullback exponential attractorsDiscret. Contin. Dyn. Syst.20102641329135726007490568550610.3934/dcds.2010.26.1329 Da PratoGZabczykJStochastic Equations in Infinite Dimensions1992CambridgeCambridge University Press0761.6005210.1017/CBO9780511666223 ChueshovIGiryaTInertial manifolds and stationary measures for stochastically perturbed dissipative dynamical systemsMat. Sb.19951861294616416640851.6003610.1070/SM1995v186n01ABEH000002 EfendievMMiranvilleAZelikSExponential attractors and finite-dimensional reduction for non-autonomous dynamical systemsProc. R. Soc. Edinb. A200513570373021733361088.3700510.1017/S030821050000408X KuksinSShirikyanAMathematics of Two-Dimensional Turbulence2012CambridgeCambridge University Press0606661110.1017/CBO9781139137119 ChueshovIScheutzowMInertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equationsJ. Dyn. Differ. Equ.200113235538018296020990.3704110.1023/A:1016684108862 KuksinSShirikyanAOn random attractors for systems of mixing typeFunct. Anal. Appl.2004381283720617891086.3702710.1023/B:FAIA.0000024865.78811.11 CrauelHFlandoliFAdditive noise destroys a pitchfork bifurcationJ. Dyn. Differ. Equ.19981025927416230130907.3404210.1023/A:1022665916629 LorentzGGApproximation of Functions1986New YorkChelsea Publishing Co.0643.41001 MiranvilleAExponential attractors for nonautonomous evolution equationsAppl. Math. Lett.19981121922160966110.1016/S0893-9659(98)00004-4 FlandoliFDissipativity and invariant measures for stochastic Navier–Stokes equationsNoDEA Nonlinear Differ. Equ. Appl.19941440342313001500820.3510810.1007/BF01194988 Eden, A., Foias, C., Nicolaenko, B., Temam, R.: Exponential attractors for dissipative evolution equations. RAM: Research in Applied Mathematics, vol. 37. Masson, Paris (1994) M Efendiev (7_CR19) 2005; 135 P Hall (7_CR23) 1980 C Foias (7_CR22) 1988; 73 7_CR27 A Miranville (7_CR30) 1998; 11 I Chueshov (7_CR7) 1995; 186 S Kuksin (7_CR25) 2004; 38 M Efendiev (7_CR17) 2000; 330 D Stroock (7_CR32) 1993 G Prato Da (7_CR15) 1992 I Karatzas (7_CR24) 1991 V Chepyzhov (7_CR8) 1997; 5 P Fabrie (7_CR20) 2004; 10 H Crauel (7_CR6) 1998; 10 S Kuksin (7_CR26) 2012 GG Lorentz (7_CR29) 1986 A Bensoussan (7_CR2) 1995; 53 A Carvalho (7_CR9) 2013 7_CR31 I Chueshov (7_CR12) 2005 R Temam (7_CR33) 1988 7_CR16 L Arnold (7_CR1) 1998 7_CR34 7_CR13 I Chueshov (7_CR10) 2001; 13 7_CR14 H Crauel (7_CR4) 1997; 9 I Chueshov (7_CR11) 2004; 19 J Langa (7_CR28) 2010; 26 AV Babin (7_CR3) 1992 F Flandoli (7_CR21) 1994; 1 H Crauel (7_CR5) 1994; 100 M Efendiev (7_CR18) 2003; 248/249 |
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| SubjectTerms | Computational Mathematics and Numerical Analysis Computational Science and Engineering Mathematics Mathematics and Statistics Numerical Analysis Partial Differential Equations Probability Theory and Stochastic Processes Statistical Theory and Methods |
| Title | Exponential attractors for random dynamical systems and applications |
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