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

Article type: Research Article

Authors: Kitavtsev, Georgy^{a; *} | Taranets, Roman M.^b

Affiliations: [a] Middle East Technical University, Northern Cyprus Campus, KKTC, Turkey | [b] Institute of Applied Mathematics and Mechanics of the NASU, Ukraine

Correspondence: [*] Corresponding author: Georgy Kitavtsev, Middle East Technical University, Northern Cyprus Campus, Kalkanli, Güzelyurt, KKTC, 10 Mersin, Turkey. E-mail: georgy.kitavtsev@gmail.com.

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.

Keywords: Asymptotic decay, steady states, porous medium, singular diffusion

DOI: 10.3233/ASY-231884

Journal: Asymptotic Analysis, vol. 137, no. 3-4, pp. 153-176, 2024