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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.