Asymptotics for conservation laws involving Lévy diffusion generators

Tom 148 / 2001

Piotr Biler, Grzegorz Karch, Wojbor A. Woyczyński Studia Mathematica 148(2001), 171-192 MSC: 35K, 35B40, 35Q, 60H. DOI: 10.4064/sm148-2-5

Streszczenie

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.

Autorzy

  • Piotr BilerInstytut Matematyczny
    Uniwersytet Wroc/lawski
    Pl. Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail
  • Grzegorz KarchInstytut Matematyczny
    Uniwersytet Wroc/lawski
    Pl. Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail
  • Wojbor A. WoyczyńskiDepartment of Statistics and Center for Stochastic
    and Chaotic Processes in Science and Technology
    Case Western Reserve University
    Cleveland, OH 44106-7054, U.S.A.
    e-mail

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