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

KITAVTSEV G., Taranets R. M.

ASYMPTOTIC ANALYSIS, vol.137, no.3-4, pp.153-176, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 137 Issue: 3-4
  • Publication Date: 2024
  • Doi Number: 10.3233/asy-231884
  • Journal Name: ASYMPTOTIC ANALYSIS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.153-176
  • Middle East Technical University Northern Cyprus Campus Affiliated: Yes

Abstract

We analyze long-time behavior of solutions to a class of problems related to very fast and singular diffusion porous medium equations having non-homogeneous 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 H-1-convergence of the solutions to a unique non-homogeneous positive steady state generally to hold.