Displaying similar documents to “Asymptotic stability of the extended Tjon-Wu model.”

On exponential convergence to a stationary measure for a class of random dynamical systems

Sergei B. Kuksin (2001)

Journées équations aux dérivées partielles

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For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.

Strong and weak solutions to stochastic inclusions

Michał Kisielewicz (1995)

Banach Center Publications

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Existence of strong and weak solutions to stochastic inclusions x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ ℝ n H τ , z ( x τ ) q ( d τ , d z ) and x t - x s ∈ ∫ s t F τ ( x τ ) d τ + ∫ s t G τ ( x τ ) d w τ + ∫ s t ∫ | z | ≤ 1 H τ , z ( x τ ) q ( d τ , d z ) + ∫ s t ∫ | z | > 1 H τ , z ( x τ ) p ( d τ , d z ) , where p and q are certain random measures, is considered.

Asymptotic behaviour of a transport equation

Ryszard Rudnicki (1992)

Annales Polonici Mathematici

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We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation u t + b u x + c u = a ∫ 0 a x u ( t , a x - y ) μ ( d y ) . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.

Σ -convergence.

Nguetseng, Gabriel, Svanstedt, Nils (2011)

Banach Journal of Mathematical Analysis [electronic only]

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Existence of mild solutions for semilinear equation of evolution

Anna Karczewska, Stanisław Wędrychowicz (1996)

Commentationes Mathematicae Universitatis Carolinae

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The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of the results obtained to control theory is also shown. The main theorem of the paper allows to characterize...