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Asymptotic stability of a partial differential equation with an integral perturbation

Katarzyna Pichór

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 1, page 83-96
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Katarzyna Pichór. "Asymptotic stability of a partial differential equation with an integral perturbation." Annales Polonici Mathematici 68.1 (1998): 83-96. <http://eudml.org/doc/270332>.

@article{KatarzynaPichór1998,
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.},
author = {Katarzyna Pichór},
journal = {Annales Polonici Mathematici},
keywords = {integro-differential equation; Markov semigroup; asymptotic stability},
language = {eng},
number = {1},
pages = {83-96},
title = {Asymptotic stability of a partial differential equation with an integral perturbation},
url = {http://eudml.org/doc/270332},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Katarzyna Pichór
TI - Asymptotic stability of a partial differential equation with an integral perturbation
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 1
SP - 83
EP - 96
AB - 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.
LA - eng
KW - integro-differential equation; Markov semigroup; asymptotic stability
UR - http://eudml.org/doc/270332
ER -

References

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  1. [1] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1968. 
  2. [2] S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold, New York, 1969. 
  3. [3] J. Klaczak, Stability of a transport equation, Ann. Polon. Math. 49 (1988), 69-80. Zbl0673.45009
  4. [4] M. Krzyżański, Partial Differential Equations of Second Order, Vol. I, PWN, Warszawa, 1971. 
  5. [5] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994. 
  6. [6] J. Malczak, Weak and strong convergence of L¹ solutions of a transport equation, Bull. Polish. Acad. Sci. Math. 40 (1992), 59-72. Zbl0755.45021
  7. [7] K. Pichór and R. Rudnicki, Asymptotic behaviour of Markov semigroups and applications to transport equations, Bull. Polish. Acad. Sci. Math. 45 (1997), 379-397. Zbl0909.47032
  8. [8] K. Pichór and R. Rudnicki, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., to appear. Zbl0892.35072
  9. [9] R. Rudnicki, Asymptotic behaviour of a transport equation, Ann. Polon. Math. 57 (1992), 45-55. Zbl0758.45009
  10. [10] R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245-262. Zbl0838.47040

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