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ArticleOriginal scientific text

Title

Asymptotics for multifractal conservation laws

Authors 1, 1, 2

Affiliations

  1. Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  2. Department of Statistics and Center for Stochastic and Chaotic Processes in Science and Technology, Case Western Reserve University, Cleveland, Ohio 44106-7054 U.S.A.

Abstract

We study asymptotic behavior of solutions to multifractal Burgers-type equation ut+f(u)x=Au, where the operator A is a linear combination of fractional powers of the second derivative -∂2∂x2 and f is a polynomial nonlinearity. Such equations appear in continuum mechanics as models with fractal diffusion. The results include decay rates of the Lp-norms, 1 ≤ p ≤ ∞, of solutions as time tends to infinity, as well as determination of two successive terms of the asymptotic expansion of solutions.

Keywords

ENG
generalized Burgers equation, fractal diffusion, asymptotics of solutions

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Studia Mathematica
1999/135/3
Export to PBN, Opens in new tab
Pages:
231-252
Main language of publication
English
Received
1998-09-24
Published
1999
Exact and natural sciences