Displaying similar documents to “Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws”

Asymptotics for multifractal conservation laws

Piotr Biler, Grzegorz Karch, Wojbor Woyczynski (1999)

Studia Mathematica

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We study asymptotic behavior of solutions to multifractal Burgers-type equation u t + f ( u ) x = A u , 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. ...