Displaying similar documents to “On the long-time behaviour of a class of parabolic SPDE's: monotonicity methods and exchange of stability”

Uniform attractors in sup-norm for semi linear parabolic problem and application to the robust stability theory

Oleksiy Kapustyan, Olena Kapustian, Oleksandr Stanzytskyi, Ihor Korol (2023)

Archivum Mathematicum

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In this paper we establish the existence of the uniform attractor for a semi linear parabolic problem with bounded non autonomous disturbances in the phase space of continuous functions. We applied obtained results to prove the asymptotic gain property with respect to the global attractor of the undisturbed system.

On the long-time behaviour of a class of parabolic SPDE’s : monotonicity methods and exchange of stability

Benjamin Bergé, Bruno Saussereau (2005)

ESAIM: Probability and Statistics

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In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first...

Invariant measures for nonlinear SPDE's: uniqueness and stability

Bohdan Maslowski, Jan Seidler (1998)

Archivum Mathematicum

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The paper presents a review of some recent results on uniqueness of invariant measures for stochastic differential equations in infinite-dimensional state spaces, with particular attention paid to stochastic partial differential equations. Related results on asymptotic behaviour of solutions like ergodic theorems and convergence of probability laws of solutions in strong and weak topologies are also reviewed.

Mean stability of a stochastic difference equation

Viorica Mariela Ungureanu, Sui Sun Cheng (2008)

Annales Polonici Mathematici

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A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces....