Large time behavior of ODE type solutions to parabolic p-Laplacian type equations

Junyong Eom, Ryuichi Sato

Research output: Contribution to journalArticlepeer-review

Abstract

Let u be a solution to the Cauchy problem for a nonlinear diffusion equation (Equation Presented), where N ≥ 1, 2N=(N + 1) < p ≠= 2, α ∈ (-∞, 1), λ > 0 and φ ∈ BC(RN) ∩ L1(RN) with φ ≥ 0 in RN. Then the solution u behaves like a positive solution to ODE ζ′ = ζαin (0,∞). In this paper we show that the large time behavior of the solution u is described by a rescaled Barenblatt solution.

Original languageEnglish
Pages (from-to)4373-4386
Number of pages14
JournalCommunications on Pure and Applied Analysis
Volume19
Issue number9
DOIs
Publication statusPublished - 2020 Jun

Keywords

  • -Laplacian equation
  • Large time behavior
  • Nonlinear diffusion equation
  • ODE type solutions
  • Sublinear

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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