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

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KITAVTSEV G., Taranets R. M.

Asymptotic Analysis, vol.137, no.3-4, pp.153-176, 2024 (SCI-Expanded) 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, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.153-176
  • Keywords: Asymptotic decay, porous medium, singular diffusion, steady states
  • Middle East Technical University 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 H1-convergence of the solutions to a unique non-homogeneous positive steady state generally to hold.