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ArticleOriginal scientific text

Title

On the strong convergence to equilibrium of the Foiaş solutions of the transport equation

Authors 1

Affiliations

  1. Institute of Informatics, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland

Abstract

We define the Foiaş solutions of the transport equation and we prove that the strong asymptotic stability of the Foiaş solutions is equivalent to the asymptotic stability of the solutions of the transport equation in L¹.

Keywords

ENG
transport equation, Foiaş solution, Markov operator, asymptotic stability

Bibliography

  1. [DuSc] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience Publ., New York 1968.
  2. [DłLa] T. Dłotko and A. Lasota, Statistical stability and the lower bound function technique, in: Semigroups, Theory and Applications, Vol. I, H. Brezis, M. Crandall and F. Kappel (eds.), Longman Scientific and Technical, 1987, 75-95.
  3. [Klac] J. Klaczak, Stability of a transport equation, Ann. Polon. Math. 49 (1988), 69-80.
  4. [LaMa] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, 1985.
Annales Polonici Mathematici
1992/57/2
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Pages:
193-203
Main language of publication
English
Received
1992-01-13
Accepted
1992-02-18
Published
1992
Exact and natural sciences