Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains

Stationary Process ◽

Unbounded Domains ◽

Pullback Attractors ◽

Multiplicative White Noise ◽

The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations of stochastic degenerate parabolic equations. We then prove that the attractors of Wong–Zakai approximations converge to the attractor of stochastic degenerate parabolic equations driven by multiplicative white noise.

Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.03.037 ◽

2014 ◽

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pp. 1018-1038 ◽

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Author(s):

Andrew Krause ◽

Bixiang Wang

Keyword(s):

Parabolic Equations ◽

Unbounded Domains ◽

Pullback Attractors ◽

Global nonexistence of solutions to degenerate parabolic equations in unbounded domains

Applied Mathematics Letters ◽

10.1016/j.aml.2005.07.009 ◽

2006 ◽

Vol 19 (6) ◽

pp. 535-540

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Caisheng Chen

Keyword(s):

Parabolic Equations ◽

Unbounded Domains ◽

Global Nonexistence ◽

Nonexistence Of Solutions ◽

Uniqueness of the solutions of the cauchy problem and of boundary-value problems in unbounded domains for certain classes of nonlinear degenerate parabolic equations

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10.1007/bf01097157 ◽

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Keyword(s):

Cauchy Problem ◽

Boundary Value Problems ◽

Parabolic Equations ◽

Boundary Value ◽

Unbounded Domains ◽

The Cauchy Problem ◽

Nonlinear Degenerate Parabolic Equations ◽

Degenerate Parabolic ◽

Nonlinear Degenerate

Existence and uniqueness of renormalized solutions for a class of degenerate parabolic equations

Acta Mathematica Scientia ◽

10.1016/s0252-9602(09)60026-6 ◽

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Vol 29 (2) ◽

pp. 251-264 ◽

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Author(s):

Zhang Liqin ◽

Zhao Junning

Keyword(s):

Parabolic Equations ◽

Renormalized Solutions ◽

Global Attractors for Degenerate Parabolic Equations on Unbounded Domains

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10.1006/jdeq.1996.0117 ◽

1996 ◽

Vol 129 (2) ◽

pp. 239-261 ◽

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Author(s):

E. Feireisl ◽

Ph. Laurençot ◽

F. Simondon

Keyword(s):

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Unbounded Domains ◽

Global Attractors ◽

Existence and uniqueness of regular solutions of the first boundary-value problem for second-order quasilinear degenerate parabolic equations

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10.1007/bf01103719 ◽

1984 ◽

Vol 27 (2) ◽

pp. 2586-2597

Author(s):

A. V. Ivanov

Keyword(s):

Boundary Value Problem ◽

Parabolic Equations ◽

Boundary Value ◽

Second Order ◽

Regular Solutions ◽

Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity

Journal of Mathematical Sciences ◽

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2008 ◽

Vol 150 (5) ◽

pp. 2289-2301 ◽

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S. I. Shmarev

Keyword(s):

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Variable Exponents ◽

Uniqueness Of Solutions ◽

ON EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS OF QUASILINEAR DEGENERATE PARABOLIC EQUATIONS IN UNBOUNDED DOMAINS

More Progresses in Analysis ◽

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2009 ◽

Author(s):

S. BONAFEDE ◽

F. NICOLOSI

Keyword(s):

Asymptotic Behavior ◽

Parabolic Equations ◽

Unbounded Domains ◽

Existence and uniqueness of a renormalized solution for nonlinear degenerate parabolic equations with diffuse measure data

Monatshefte für Mathematik ◽

10.1007/s00605-019-01299-1 ◽

2019 ◽

Vol 190 (2) ◽

pp. 245-260 ◽

Cited By ~ 1

Author(s):

A. Bouajaja ◽

A. Marah ◽

H. Redwane

Keyword(s):

Parabolic Equations ◽

Measure Data ◽

Renormalized Solution ◽

Diffuse Measure ◽

Nonlinear Degenerate Parabolic Equations ◽

Degenerate Parabolic ◽

Nonlinear Degenerate

Pullback attractors for multi-valued non-compact random dynamical systems generated by semi-linear degenerate parabolic equations with unbounded delays

Stochastics and Dynamics ◽

10.1142/s0219493717500010 ◽

2016 ◽

Vol 16 (05) ◽

pp. 1750001 ◽

Cited By ~ 5

Author(s):

Jingyu Wang ◽

Yejuan Wang ◽

Dun Zhao

Keyword(s):

Dynamical Systems ◽

Parabolic Equations ◽

Random Dynamical Systems ◽

Pullback Attractors ◽

Asymptotic Compactness ◽

Unbounded Delay ◽

Bounded Set ◽

Degenerate Parabolic ◽

Linear Degenerate

The theory of pullback attractors for multi-valued non-compact random dynamical systems and a method of asymptotic compactness based on the concepts of the Kuratowski measure of the non-compactness of a bounded set are used to prove the existence of pullback attractors for the multi-valued non-compact random dynamical systems associated with the semi-linear degenerate parabolic unbounded delay equations with both deterministic and random external terms.