WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR CONVECTION-DIFFUSION EQUATIONS IN UNIFORMLY LOCAL LEBESGUE SPACES

被引：0

作者：

Haque, M. D. Rabiul ^{[1
]}

Ioku, Norisuke ^{[1
]}

Ogawa, Takayoshi ^{[1
,2
]}

Sato, Ryuichi ^{[2
]}

机构：

[1] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

[2] Tohoku Univ, Res Alliance Ctr Math Anal, Sendai, Miyagi 9808578, Japan

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2021年 / 34卷 / 3-4期

关键词：

LARGE TIME BEHAVIOR; LINEAR PARABOLIC EQUATIONS; HEAT-EQUATION; R-N; EXISTENCE; NONEXISTENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the well-posedness of the Cauchy problem for convection-diffusion equations in uniformly local Lebesgue spaces L-uloc(r)(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-uloc(p) - L-uloc(q) estimate for the heat semigroup obtained by Maekawa-Terasawa [20], the Banach fixed point theorem, and the comparison principle.

引用

页码：223 / 244

页数：22

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