Asymptotics for multifractal conservation laws

Volume 135 / 1999

Piotr Biler, , Studia Mathematica 135 (1999), 231-252 DOI: 10.4064/sm-135-3-231-252


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.


  • Piotr Biler

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