✦ LIBER ✦
Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
✍ Scribed by Piotr Biler; Grzegorz Karch; Wojbor A Woyczyński
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 188 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0294-1449
No coin nor oath required. For personal study only.
✦ Synopsis
Nonlocal conservation laws of the form
where -L is the generator of a Lévy semigroup on L 1 (R n ), are encountered in continuum mechanics as model equations with anomalous diffusion. They are generalizations of the classical Burgers equation. We study the critical case when the diffusion and nonlinear terms are balanced, e.g. L ∼ (-) α/2 , 1 < α < 2, f (s) ∼ s|s| r-1 , r = 1 + (α -1)/n. The results include decay rates of solutions and their genuinely nonlinear asymptotic behavior as time t tends to infinity, determined by self-similar source solutions.