Translator Disclaimer
March/April 2021 Well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces
Md. Rabiul Haque, Norisuke Ioku, Takayoshi Ogawa, Ryuichi Sato
Differential Integral Equations 34(3/4): 223-244 (March/April 2021).

Abstract

We consider the well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces $L^r_{\text{uloc}}(\mathbb R^n)$. 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 $L^p_{\text{uloc}}- L^q_{\text{uloc}}$ estimate for the heat semigroup obtained by Maekawa--Terasawa [20], the Banach fixed point theorem, and the comparison principle.

Citation

Download Citation

Md. Rabiul Haque. Norisuke Ioku. Takayoshi Ogawa. Ryuichi Sato. "Well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces." Differential Integral Equations 34 (3/4) 223 - 244, March/April 2021.

Information

Published: March/April 2021
First available in Project Euclid: 8 May 2021

Subjects:
Primary: 35A01 , 35K58 , 35Q30 , 76D05

Rights: Copyright © 2021 Khayyam Publishing, Inc.

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.34 • No. 3/4 • March/April 2021
Back to Top