Geodesic
Asymptotic behaviour of a transport equation
Annales Polonici Mathematici, Tome 57 (1992) no. 1, pp. 45-55

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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. 
Ryszard Rudnicki. Asymptotic behaviour of a transport equation. Annales Polonici Mathematici, Tome 57 (1992) no. 1, pp. 45-55. doi: 10.4064/ap-57-1-45-55
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