Asymptotic behaviour of a transport equation
Tom 57 / 1992
Annales Polonici Mathematici 57 (1992), 45-55
DOI: 10.4064/ap-57-1-45-55
Streszczenie
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.
