Asymptotics for conservation laws involving Lévy diffusion generators

• Autorzy: Piotr Biler , Grzegorz Karch , Wojbor A. Woyczyński
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 148
• Numer: 2
• Strony: 171-192

Daty

wydano

2001

Twórcy

autor

Piotr Biler

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Grzegorz Karch

• Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Wojbor A. Woyczyński

• Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, Cleveland, OH 44106-7054, U.S.A.

Identyfikatory

DOI

10.4064/sm148-2-5