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Rarefaction waves in nonlocal convection-diffusion equations

Volume 137 / 2014

Anna Pudełko 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.

Authors

  • Anna PudełkoAGH University of Science and Technology
    Al. Mickiewicza 30
    30-059 Kraków, Poland
    e-mail

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