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

Jan Malczak

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 2, page 193-203
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Jan Malczak. "On the strong convergence to equilibrium of the Foiaş solutions of the transport equation." Annales Polonici Mathematici 57.2 (1992): 193-203. <http://eudml.org/doc/262380>.

@article{JanMalczak1992,
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.},
author = {Jan Malczak},
journal = {Annales Polonici Mathematici},
keywords = {transport equation; Foiaş solution; Markov operator; asymptotic stability; strong convergence; strongly asymptotical stability; Foiaş solutions; integro-differential equation; Markov operators; Foiaş operators},
language = {eng},
number = {2},
pages = {193-203},
title = {On the strong convergence to equilibrium of the Foiaş solutions of the transport equation},
url = {http://eudml.org/doc/262380},
volume = {57},
year = {1992},
}

TY - JOUR
AU - Jan Malczak
TI - On the strong convergence to equilibrium of the Foiaş solutions of the transport equation
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 2
SP - 193
EP - 203
AB - 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.
LA - eng
KW - transport equation; Foiaş solution; Markov operator; asymptotic stability; strong convergence; strongly asymptotical stability; Foiaş solutions; integro-differential equation; Markov operators; Foiaş operators
UR - http://eudml.org/doc/262380
ER -

References

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  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. Zbl0673.45009
  4. [LaMa] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, 1985. Zbl0606.58002

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