Displaying similar documents to “Asymptotic stability of a partial differential equation with an integral perturbation”

Asymptotic stability in L¹ of a transport equation

M. Ślęczka (2004)

Annales Polonici Mathematici

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We study the asymptotic behaviour of solutions of a transport equation. We give some sufficient conditions for the complete mixing property of the Markov semigroup generated by this equation.

Asymptotic stability of a linear Boltzmann-type equation

Roksana Brodnicka, Henryk Gacki (2014)

Applicationes Mathematicae

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We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.

Randomly connected dynamical systems - asymptotic stability

Katarzyna Horbacz (1998)

Annales Polonici Mathematici

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We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.

Asymptotic Stability of Zakharov-Kuznetsov solitons

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.

A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces

Dawid Czapla (2012)

Annales Polonici Mathematici

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Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space...

Stability for dissipative magneto-elastic systems

Reinhard Racke (2003)

Banach Center Publications

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In this survey we first recall results on the asymptotic behavior of solutions in classical thermoelasticity. Then we report on recent results in linear magneto-thermo-elasticity and magneto-elasticity, respectively.

New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations

Mimia Benhadri, Tomás Caraballo (2022)

Mathematica Bohemica

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This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.

Dynamics and density evolution in piecewise deterministic growth processes

Michael C. Mackey, Marta Tyran-Kamińska (2008)

Annales Polonici Mathematici

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A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence of a unique stationary density and give sufficient conditions for asymptotic stability.

Applications of the Kantorovich-Rubinstein maximum principle in the theory of Markov semigroups

Henryk Gacki

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We present new sufficient conditions for the asymptotic stability of Markov operators acting on the space of signed measures. Our results are based on two principles. The first one is the LaSalle invariance principle used in the theory of dynamical systems. The second is related to the Kantorovich-Rubinstein theorems concerning the properties of probability metrics. These criteria are applied to stochastically perturbed dynamical systems, a Poisson driven stochastic differential equation...

A complete description of dynamics generated by birth-and-death problem: a semigroup approach

Jacek Banasiak (2003)

Banach Center Publications

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We shall present necessary and sufficient conditions for both conservativity and uniqueness of solutions to birth-and-death system of equations using methods of semigroup theory. The derived conditions correspond to the uniqueness criteria for forward and backward birth-and-death systems due to Reuter, [10,11,1], that were derived in a different context by Markov processes' techniques.