Rarefaction waves in nonlocal convection-diffusion equations

Anna Pudelko

Rarefaction waves in nonlocal convection-diffusion equations

Analysis of PDEs 2013-04-17 v2

Authors: Anna Pudelko

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.

Keywords

nonlinear diffusion equations shock waves advection-diffusion equations

Cite

@article{arxiv.1304.0045,
  title  = {Rarefaction waves in nonlocal convection-diffusion equations},
  author = {Anna Pudelko},
  journal= {arXiv preprint arXiv:1304.0045},
  year   = {2013}
}

Comments

17 pages. arXiv admin note: text overlap with arXiv:math/0702088 by other authors

Related papers

View all related →