Asymptotic behaviour of a transport equation

• Autorzy: Ryszard Rudnicki
• Języki publikacji: EN

Abstrakty

EN

We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation $u_t + bu_x + cu = a∫_0^{ax} u(t,ax-y)μ(dy)$. We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.

Kategorie tematyczne

• 45K05: Integro-partial differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 1
• Strony: 45-55

Daty

wydano

1992

otrzymano

1991-01-02

Twórcy

autor

Ryszard Rudnicki

• Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8, 40-013 Katowice, Poland

Bibliografia

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• [2] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience Publ., New York 1968.
• [3] J. Klaczak, Stability of a transport equation, Ann. Polon. Math. 49 (1988), 69-80.
• [4] A. Lasota and J. A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384.
• [5] K. Łoskot, Stochastic perturbations of dynamical systems, Ann. Polon. Math., to appear.
• [6] A. Rényi, Probability Theory, Akadémiai Kiadó, Budapest 1970.
• [7] A. N. Shiryaev, Probability, Nauka, Moscow 1989 (in Russian).