# Far field asymptotics of solutions to convection equation with anomalous diffusion

1 ICJ - Institut Camille Jordan Villeurbanne 2 Instytut Matematyczny

Abstract : The initial value problem for the conservation law $\partial t u+-\Delta^{\alpha-2}u+ abla \cdot fu=0$ is studied for $\alpha\in 1,2$ and under natural polynomial growth conditions imposed on the nonlinearity. We find the asymptotic expansion as $|x|\to \infty$ of solutions to this equation corresponding to initial conditions, decaying sufficiently fast at infinity.

Mots-clés : Anomalous diffusion asymptotic profiles self-similar solutions decay estimates fractal Burgers equation conservation laws

Author: Lorenzo Brandolese - Grzegorz Karch -

Source: https://hal.archives-ouvertes.fr/