Asymptotic stability of an integro-differential equation of parabolic type
Danuta Jama (1986)
Annales Polonici Mathematici
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Danuta Jama (1986)
Annales Polonici Mathematici
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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...
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.
Piotr Biler (1989)
Colloquium Mathematicae
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Tunç, Cemil (2005)
Journal of Applied Mathematics and Stochastic Analysis
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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....
Didier Pilod (2014-2015)
Séminaire Laurent Schwartz — EDP et applications
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In this report, we review the proof of the asymptotic stability of the Zakharov-Kuznetsov solitons in dimension two. Those results were recently obtained in a joint work with Raphaël Côte, Claudio Muñoz and Gideon Simpson.
Kleber Carrapatoso (2014-2015)
Séminaire Laurent Schwartz — EDP et applications
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I present in this note recent results on the uniqueness and stability for the parabolic-parabolic Keller-Segel equation on the plane, obtained in collaboration with S. Mischler in [11].
Changchun Liu, Jinyong Guo (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.