Asymptotic decay towards steady states of solutions to very fast and singular diffusion equations
Asymptotic Analysis, vol.137, no.3-4, pp.153-176, 2024 (SCI-Expanded, Scopus)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.