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

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

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 223-244 22 Differential and Integral Equations 34 3-4 Published - 2021

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• 応用数学

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