Asymptotics for conservation laws involving Lévy diffusion generators
Volume 148 / 2001
Studia Mathematica 148 (2001), 171-192
MSC: 35K, 35B40, 35Q, 60H.
DOI: 10.4064/sm148-2-5
Abstract
Let $-{\cal L}$ be the generator of a Lévy semigroup on $L^1({\mathbb R}^n)$ and $f:{\mathbb R}\to {\mathbb R}^n$ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations $u_t+{\cal L}u+\nabla \cdot f(u)=0$, analyzing their $L^p$-decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.
