ArticleOriginal scientific text
Title
Asymptotic stability of a partial differential equation with an integral perturbation
Authors 1
Affiliations
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Abstract
We study the asymptotic behaviour of the Markov semigroup generated by an integro-partial differential equation. We give new sufficient conditions for asymptotic stability of this semigroup.
Keywords
integro-differential equation, Markov semigroup, asymptotic stability
Bibliography
- N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1968.
- S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold, New York, 1969.
- J. Klaczak, Stability of a transport equation, Ann. Polon. Math. 49 (1988), 69-80.
- M. Krzyżański, Partial Differential Equations of Second Order, Vol. I, PWN, Warszawa, 1971.
- A. Lasota and M. C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994.
- J. Malczak, Weak and strong convergence of L¹ solutions of a transport equation, Bull. Polish. Acad. Sci. Math. 40 (1992), 59-72.
- K. Pichór and R. Rudnicki, Asymptotic behaviour of Markov semigroups and applications to transport equations, Bull. Polish. Acad. Sci. Math. 45 (1997), 379-397.
- K. Pichór and R. Rudnicki, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., to appear.
- R. Rudnicki, Asymptotic behaviour of a transport equation, Ann. Polon. Math. 57 (1992), 45-55.
- R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245-262.
Pages:
83-96
Main language of publication
English
Received
1997-05-13
Accepted
1997-07-08
Published
1998
Exact and natural sciences