Asymptotics for conservation laws involving Lévy diffusion generators

Piotr Biler; Grzegorz Karch; Wojbor A. Woyczyński

Studia Mathematica (2001)

  • Volume: 148, Issue: 2, page 171-192
  • ISSN: 0039-3223

Abstract

top
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.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.