Asymptotics for conservation laws involving Lévy diffusion generators
Piotr Biler ; Grzegorz Karch ; Wojbor A. Woyczyński
Studia Mathematica, Tome 147 (2001), p. 171-192 / Harvested from The Polish Digital Mathematics Library
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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 Lp-decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:284484 
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     title = {Asymptotics for conservation laws involving L\'evy diffusion generators},
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     volume = {147},
     year = {2001},
     pages = {171-192},
     zbl = {0990.35023},
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Piotr Biler; Grzegorz Karch; Wojbor A. Woyczyński. Asymptotics for conservation laws involving Lévy diffusion generators. Studia Mathematica, Tome 147 (2001) pp. 171-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm148-2-5/