Asymptotics for conservation laws
involving Lévy diffusion generators
Studia Mathematica, Tome 148 (2001) no. 2, pp. 171-192
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
cal generator semigroup mathbb mathbb mathbb nonlinearity study large time asymptotic behavior solutions nonlocal nonlinear equations cal nabla cdot analyzing their p decay terms their asymptotics these equations appear models physical phenomena involve anomalous diffusions flights
Affiliations des auteurs :
Piotr Biler 1 ; Grzegorz Karch 1 ; Wojbor A. Woyczyński 2
@article{10_4064_sm148_2_5,
author = {Piotr Biler and Grzegorz Karch and Wojbor A. Woyczy\'nski},
title = {Asymptotics for conservation laws
involving {L\'evy} diffusion generators},
journal = {Studia Mathematica},
pages = {171--192},
publisher = {mathdoc},
volume = {148},
number = {2},
year = {2001},
doi = {10.4064/sm148-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm148-2-5/}
}
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Piotr Biler; Grzegorz Karch; Wojbor A. Woyczyński. Asymptotics for conservation laws involving Lévy diffusion generators. Studia Mathematica, Tome 148 (2001) no. 2, pp. 171-192. doi: 10.4064/sm148-2-5
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