Accès libre

Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

À propos de cet article

Citez

Arnold L. Random dynamical systems. Springer-Verlag: Berlin, 1998.ArnoldL.Random dynamical systems.Springer-VerlagBerlin199810.1007/978-3-662-12878-7Search in Google Scholar

Crauel H, Flandoli F. Attractors for random dynamical systems. Probability Theory and Related Fields 1994; 100(3):365–393.10.1007/BF01193705CrauelHFlandoliF.Attractors for random dynamical systemsProbability Theory and Related Fields19941003365393Open DOISearch in Google Scholar

Schmalfuss B. Measure attractors and stochastic attractors, institut for dynamische systeme. Technical Report, Bermen University 1995.SchmalfussB.Measure attractors and stochastic attractorsinstitut for dynamische systeme. Technical ReportBermen University1995Search in Google Scholar

Crauel H, Debussche A, Flandoli F. Random attractors. Journal of Dynamics and Differential Equations 1997; 9(2):307–341.10.1007/BF02219225CrauelHDebusscheAFlandoliF.Random attractorsJournal of Dynamics and Differential Equations199792307341Open DOISearch in Google Scholar

Crauel H. Global random attractors are uniquely determined by attracting deterministic compact sets. Annali di Matematica pura ed applicata 1999; 176(1):57–72.10.1007/BF02505989CrauelH.Global random attractors are uniquely determined by attracting deterministic compact setsAnnali di Matematica pura ed applicata199917615772Open DOISearch in Google Scholar

Bates PW, Lu K, Wang B. Random attractors for stochastic reaction–diffusion equations on unbounded domains. Journal of Differential Equations 2009; 246(2):845–869.10.1016/j.jde.2008.05.017BatesPWLuKWangB.Random attractors for stochastic reaction–diffusion equations on unbounded domainsJournal of Differential Equations20092462845869Open DOISearch in Google Scholar

Chueshov ID. Gevrey regularity of random attractors for stochastic reaction-diffusion equations. Random Operators and Stochastic Equations 2000; 8(2):143–162.ChueshovID.Gevrey regularity of random attractors for stochastic reaction-diffusion equationsRandom Operators and Stochastic Equations20008214316210.1515/rose.2000.8.2.143Search in Google Scholar

Temam R. Infinite-dimensional dynamical systems in mechanics and physics. Springer-Verlag: New York, 1997.TemamR.Infinite-dimensional dynamical systems in mechanics and physics.Springer-VerlagNew York199710.1007/978-1-4612-0645-3Search in Google Scholar

Chepyzhov V, Vishik M. A hausdorff dimension estimate for kernel sections of non-autonomous evolution equations. Indiana University Mathematics Journal 1993; 42(3):1057–1076.10.1512/iumj.1993.42.42049ChepyzhovVVishikM.A hausdorff dimension estimate for kernel sections of non-autonomous evolution equationsIndiana University Mathematics Journal199342310571076Open DOISearch in Google Scholar

Caraballo T, Langa J, Valero J. The dimension of attractors of nonautonomous partial differential equations. The ANZIAM Journal 2003; 45(2):207–222.10.1017/S1446181100013274CaraballoTLangaJValeroJ.The dimension of attractors of nonautonomous partial differential equationsThe ANZIAM Journal2003452207222Open DOISearch in Google Scholar

Crauel H, Flandoli F. Hausdorff dimension of invariant sets for random dynamical systems. Journal of Dynamics and Differential Equations 1998; 10(3):449–474.10.1023/A:1022605313961CrauelHFlandoliF.Hausdorff dimension of invariant sets for random dynamical systemsJournal of Dynamics and Differential Equations1998103449474Open DOISearch in Google Scholar

Schmallfuss B. The random attractor of the stochastic lorenz system. Zeitschrift für angewandte Mathematik und Physik 1997; 48(6):951–975.10.1007/s000330050074SchmallfussB.The random attractor of the stochastic lorenz systemZeitschrift für angewandte Mathematik und Physik1997486951975Open DOISearch in Google Scholar

Debussche A. On the finite dimensionality of random attractors. Stochastic analysis and applications 1997; 15(4):473– 491.10.1080/07362999708809490DebusscheA.On the finite dimensionality of random attractorsStochastic analysis and applications1997154473491Open DOISearch in Google Scholar

Debussche A. Hausdorff dimension of a random invariant set. Journal de mathématiques pures et appliquées 1998; 77(10):967–988.10.1016/S0021-7824(99)80001-4DebusscheA.Hausdorff dimension of a random invariant setJournal de mathématiques pures et appliquées19987710967988Open DOISearch in Google Scholar

Wang B. Random attractors for non-autonomous stochastic wave equations with multiplicative noise. Discrete & Continuous Dynamical Systems-A 2014; 34(1):269–300. 10.3934/dcds.2014.34.269WangB.Random attractors for non-autonomous stochastic wave equations with multiplicative noiseDiscrete & Continuous Dynamical Systems-A201434126930010.3934/dcds.2014.34.269Open DOISearch in Google Scholar

Caraballo T, Langa JA, Robinson JC. Stability and random attractors for a reaction-diffusion equation with multiplicative noise. Discrete and Continuous Dynamical Systems 2000; 6(4):875–892.10.3934/dcds.2000.6.875CaraballoTLangaJARobinsonJC.Stability and random attractors for a reaction-diffusion equation with multiplicative noiseDiscrete and Continuous Dynamical Systems200064875892Open DOISearch in Google Scholar

Zhou S, Yin F, Ouyang Z. Random attractor for damped nonlinear wave equations with white noise. SIAM Journal on Applied Dynamical Systems 2005; 4(4):883–903. 10.1137/050623097ZhouSYinFOuyangZ.Random attractor for damped nonlinear wave equations with white noiseSIAM Journal on Applied Dynamical Systems20054488390310.1137/050623097Open DOISearch in Google Scholar

Fan X, Chen H. Attractors for the stochastic reaction–diffusion equation driven by linear multiplicative noise with a variable coefficient. Journal of Mathematical Analysis and Applications 2013; 398(2):715–728. hrefhttps://doi.org/10.1016/j.jmaa.2012.09.02710.1016/j.jmaa.2012.09.027FanXChenH.Attractors for the stochastic reaction–diffusion equation driven by linear multiplicative noise with a variable coefficientJournal of Mathematical Analysis and Applications20133982715728hrefhttps://doi.org/10.1016/j.jmaa.2012.09.02710.1016/j.jmaa.2012.09.027Open DOISearch in Google Scholar

Fan X. Attractors for a damped stochastic wave equation of sine–gordon type with sublinear multiplicative noise. Stochastic Analysis and Applications 2006; 24(4):767–793. 10.1080/07362990600751860FanX.Attractors for a damped stochastic wave equation of sine–gordon type with sublinear multiplicative noiseStochastic Analysis and Applications200624476779310.1080/07362990600751860Open DOISearch in Google Scholar

Crauel H, Flandoli F. Additive noise destroys a pitchfork bifurcation. Journal of Dynamics and Differential Equations 1998; 10(2):259–274.10.1023/A:1022665916629CrauelHFlandoliF.Additive noise destroys a pitchfork bifurcationJournal of Dynamics and Differential Equations1998102259274Open DOISearch in Google Scholar

Arnold L, Bleckert G, Schenk-Hoppé KR. The stochastic brusselator: Parametric noise destroys hoft bifurcation. Stochastic dynamics. Springer, 1999; 71–92.ArnoldLBleckertGSchenk-HoppéKR.The stochastic brusselator: Parametric noise destroys hoft bifurcationStochastic dynamics.Springer1999719210.1007/0-387-22655-9_4Search in Google Scholar

Wang B. Existence, stability and bifurcation of random complete and periodic solutions of stochastic parabolic equations. Nonlinear Analysis: Theory, Methods & Applications 2014; 103:9–25.10.1016/j.na.2014.02.013WangB.Existence, stability and bifurcation of random complete and periodic solutions of stochastic parabolic equationsNonlinear Analysis: Theory, Methods & Applications2014103925Open DOISearch in Google Scholar

Schenk-Hoppé KR. Random attractors–general properties, existence and applications to stochastic bifurcation theory. Discrete & Continuous Dynamical Systems-A 1998; 4(1):99–130.Schenk-HoppéKR.Random attractors–general properties, existence and applications to stochastic bifurcation theoryDiscrete & Continuous Dynamical Systems-A1998419913010.3934/dcds.1998.4.99Search in Google Scholar

Carslaw HS, Jaeger JC. Conduction of heat in solids. Oxford: Clarendon Press, 1959, 2nd ed. 1959;.CarslawHSJaegerJC.Conduction of heat in solids.Oxford: Clarendon Press19592nd ed1959Search in Google Scholar

Caraballo T, Langa JA, Robinson JC. A stochastic pitchfork bifurcation in a reaction-diffusion equation. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 457, The Royal Society, 2001; 2041–2061.CaraballoTLangaJARobinsonJC.A stochastic pitchfork bifurcation in a reaction-diffusion equationProceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences457The Royal Society20012041206110.1098/rspa.2001.0819Search in Google Scholar

Keller H, Ochs G. Numerical approximation of random attractors. Stochastic dynamics. Springer, 1999; 93–115.KellerHOchsG.Numerical approximation of random attractorsStochastic dynamics.Springer19999311510.1007/0-387-22655-9_5Search in Google Scholar

Protter PE. Stochastic differential equations. Stochastic integration and differential equations. Springer, 2005; 249–361.ProtterPE.Stochastic differential equationsStochastic integration and differential equations.Springer200524936110.1007/978-3-662-10061-5_6Search in Google Scholar

Crauel H. Random point attractors versus random set attractors. Journal of the London Mathematical Society 2001; 63(2):413–427.10.1017/S0024610700001915CrauelH.Random point attractors versus random set attractorsJournal of the London Mathematical Society2001632413427Open DOISearch in Google Scholar

Birnir B. Basic Attractors and Control. Springer-Verlag: New York, 2015.BirnirB.Basic Attractors and Control.Springer-VerlagNew York2015Search in Google Scholar

Debussche A, Temam R. Some new generalizations of inertial manifolds. Discrete & Continuous Dynamical Systems-A 1996; 2(4):543–558.10.3934/dcds.1996.2.543DebusscheATemamR.Some new generalizations of inertial manifoldsDiscrete & Continuous Dynamical Systems-A199624543558Open DOISearch in Google Scholar

Marion M, Temam R. Nonlinear galerkin methods. SIAM Journal on Numerical Analysis 1989; 26(5):1139–1157.10.1137/0726063MarionMTemamR.Nonlinear galerkin methodsSIAM Journal on Numerical Analysis198926511391157Open DOISearch in Google Scholar

Multiphysics A. COMSOL Multiphysics 3.5 a Reference Manual, PDE mode equation based modeling. Multiphysics Ltd: Stohkholm, Sweden, 2008.MultiphysicsA.COMSOL Multiphysics 3.5 a Reference Manual, PDE mode equation based modeling.Multiphysics LtdStohkholm, Sweden2008Search in Google Scholar

Kloeden P, Eckhard P. Numerical solution of stochastic differential equations. Springer-Verlag: Berlin, 1992.KloedenPEckhardP.Numerical solution of stochastic differential equations.Springer-VerlagBerlin199210.1007/978-3-662-12616-5Search in Google Scholar

eISSN:
2444-8656
Langue:
Anglais
Périodicité:
Volume Open
Sujets de la revue:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics