Existence of weak solutions to a convection–diffusion equation in a uniformly local Lebesgue space

Md Rabiul Haque, Takayoshi Ogawa, Ryuichi Sato

Research output: Contribution to journalArticle

Abstract

We consider the local existence and the uniqueness of a weak solution of the initial boundary value problem to a convection–diffusion equation in a uniformly local function space Lr uloc,ρ(Ω), where the solution is not decaying at |x| → ∞. We show that the local existence and the uniqueness of a solution for the initial data in uniformly local Lr spaces and identify the Fujita-Weissler critical exponent for the local well-posedness found by Escobedo-Zuazua [10] is also valid for the uniformly local function class.

Original languageEnglish
Pages (from-to)677-697
Number of pages21
JournalCommunications on Pure and Applied Analysis
Volume19
Issue number2
DOIs
Publication statusPublished - 2020 Jan 1

Keywords

  • Convection-diffusion equation
  • Uniformly local Lebesgue spaces
  • Weak solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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