Asymptotics for conservation laws involving Lévy diffusion generators

Piotr Biler, Grzegorz Karch, and Wojbor A. Woyczyński. "Asymptotics for conservation laws involving Lévy diffusion generators." Studia Mathematica 148.2 (2001): 171-192. <http://eudml.org/doc/284484>.

@article{PiotrBiler2001,
abstract = {Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·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.},
author = {Piotr Biler, Grzegorz Karch, Wojbor A. Woyczyński},
journal = {Studia Mathematica},
keywords = {generalized Burgers equation; Lévy diffusion; asymptotics of solutions; Lévy flights; anomalous diffusion; pseudo differential operator; Lévy conservation laws},
language = {eng},
number = {2},
pages = {171-192},
title = {Asymptotics for conservation laws involving Lévy diffusion generators},
url = {http://eudml.org/doc/284484},
volume = {148},
year = {2001},
}

TY - JOUR
AU - Piotr Biler
AU - Grzegorz Karch
AU - Wojbor A. Woyczyński
TI - Asymptotics for conservation laws involving Lévy diffusion generators
JO - Studia Mathematica
PY - 2001
VL - 148
IS - 2
SP - 171
EP - 192
AB - Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·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.
LA - eng
KW - generalized Burgers equation; Lévy diffusion; asymptotics of solutions; Lévy flights; anomalous diffusion; pseudo differential operator; Lévy conservation laws
UR - http://eudml.org/doc/284484
ER -