English

Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations

Analysis of PDEs 2022-10-24 v1

Abstract

We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having nonhomogeneous in space and time source terms with zero mean. In dimensions two and three, we determine critical values of porous medium exponent for the asymptotic H1H^1-convergence of the solutions to a unique nonhomogeneous positive steady state generally to hold.

Keywords

Cite

@article{arxiv.2210.12025,
  title  = {Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations},
  author = {Georgy Kitavtsev and Roman M. Taranets},
  journal= {arXiv preprint arXiv:2210.12025},
  year   = {2022}
}