Existence of solutions to the slow diffusion equation with a nonlinear source

Ryuichi Sato

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider the existence of solutions to Cauchy problem for the slow diffusion equation with a source term ∂tu=Δum+up, x∈RN, t>0, u(x,0)=φ(x)≥0, where m≥1 and p>m. Our purpose is to obtain lower estimates of the existence time of solutions in the uniformly local Lebesgue spaces. Furthermore, we obtain the estimate of blow-up time, blow-up rate of solutions and blow-up of critical norm.

Original languageEnglish
Article number123721
JournalJournal of Mathematical Analysis and Applications
Volume484
Issue number2
DOIs
Publication statusPublished - 2020 Apr 15

Keywords

  • Existence of solutions
  • Quasilinear parabolic equation
  • Uniformly Lebesgue spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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