Asymptotics for multifractal conservation laws

Biler, Piotr ; Karch, Grzegorz ; Woyczynski, Wojbor

Studia Mathematica, Tome 133 (1999), p. 231-252 / Harvested from The Polish Digital Mathematics Library

Résumé

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

Détail

Publié le : 1999-01-01

Zbl 0931.35015

EUDML-ID : urn:eudml:doc:216653

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