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

2022/10/21 by Georgy Kitavtsev, Kitavtsev, Georgy, Roman M. Taranets +1
Computer Science · Mathematics · #35B40 #35G31 #35K59 #76D27 #76D45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.12025

openalex publication_date 2022/10/21 · openalex created_date 2022/10/30 · openalex updated_date 2026/07/28

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 H¹-convergence of the solutions to a unique nonhomogeneous positive steady state generally to hold.

Related

• Large time behavior for a porous medium equation in a nonhomogeneous\n medium with critical density
• New Lipschitz estimates and long-time asymptotic behavior for porous medium and fast diffusion equations
• Asymptotic behavior for the critical nonhomogeneous porous medium\n equation in low dimensions
• Asymptotic large time behavior of singular solutions of the fast diffusion equation
• Fundamental solution and long time behaviour of the Porous Medium\n Equation in Hyperbolic Space