Rarefaction waves in nonlocal convection-diffusion equations
Volume 137 / 2014
Colloquium Mathematicum 137 (2014), 27-42
MSC: Primary 35B40; Secondary 35K55.
DOI: 10.4064/cm137-1-3
Abstract
We consider a nonlocal convection-diffusion 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 the convergence of the corresponding solutions towards a rarefaction wave, i.e. a unique entropy solution of the Riemann problem for the inviscid Burgers equation.
