Geodesic
Asymptotics for conservation laws involving Lévy diffusion generators
Piotr Biler1 ; Grzegorz Karch1 ; Wojbor A. Woyczyński2
1Instytut Matematyczny Uniwersytet Wroc/lawski Pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
2Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology Case Western Reserve University Cleveland, OH 44106-7054, U.S.A.
Studia Mathematica, Tome 148 (2001) no. 2, pp. 171-192
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm148-2-5
Keywords: cal generator semigroup mathbb mathbb mathbb nonlinearity study large time asymptotic behavior solutions nonlocal nonlinear equations cal nabla cdot analyzing their p decay terms their asymptotics these equations appear models physical phenomena involve anomalous diffusions flights

Piotr Biler  1   ; Grzegorz Karch  1   ; Wojbor A. Woyczyński  2

1 Instytut Matematyczny Uniwersytet Wroc/lawski Pl. Grunwaldzki 2/4 50-384 Wroc/law, Poland
2 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. 
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     title = {Asymptotics for conservation laws
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involving Lévy diffusion generators
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Piotr Biler; Grzegorz Karch; Wojbor A. Woyczyński. Asymptotics for conservation laws
involving Lévy diffusion generators. Studia Mathematica, Tome 148 (2001) no. 2, pp. 171-192. doi: 10.4064/sm148-2-5

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