Well-posedness of the cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces

Md Rabiul Haque, Norisuke Ioku, Takayoshi Ogawa, Ryuichi Sato

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces Lruloc(ℝn). In our setting, an initial function that is spatially periodic or converges to a nonzero constant at infinity is admitted. Our result is applicable to the one dimensional viscous Burgers equation. For the proof, we use the Lpuloc −Lquloc estimate for the heat semigroup obtained by Maekawa-Terasawa [20], the Banach fixed point theorem, and the comparison principle.

Original languageEnglish
Pages (from-to)223-244
Number of pages22
JournalDifferential and Integral Equations
Volume34
Issue number3-4
Publication statusPublished - 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Well-posedness of the cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces'. Together they form a unique fingerprint.

Cite this