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

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

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)223-244
ページ数22
ジャーナルDifferential and Integral Equations
34
3-4
出版ステータスPublished - 2021

ASJC Scopus subject areas

  • 分析
  • 応用数学

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