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arXiv · 1304.0045

Rarefaction waves in nonlocal convection-diffusion equations

Anna Pudelko
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Abstract

We consider the "convection-diffussion" equation $u_t=J*u-u-uu_x,$ where $J$ is a probability density. We supplement this equation with step-like initial conditions and prove a convergence of corresponding solution towards a rarefaction wave, i.e. a unique entropy solution of the Riemann problem for the nonviscous Burgers equation. Methods and tools used in this paper are inspired by those used in [Karch, Miao and Xu, SIAM J. Math. Anal. {\bf 39} (2008), no. 5, 1536--1549.], where the fractal Burgers equation was studied.

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Anna Pudelko. 2013-03-29. Rarefaction waves in nonlocal convection-diffusion equations. https://arxiv.org/abs/1304.0045

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