English

Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity

Analysis of PDEs 2019-05-24 v1

Abstract

We consider the singular limit of a bistable reaction diffusion equation in the case when the velocity of the traveling wave solution depends on the space variable and converges to a discontinuous function. We show that the family of solutions converges to the stable equilibria off a front propagating with a discontinuous velocity. The convergence is global in time by applying the weak geometric flow uniquely defined through the theory of viscosity solutions and the level-set equation.

Keywords

Cite

@article{arxiv.1905.09583,
  title  = {Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity},
  author = {Cecilia De Zan and Pierpaolo Soravia},
  journal= {arXiv preprint arXiv:1905.09583},
  year   = {2019}
}