# Existence of weak solutions to a convection–diffusion equation in a uniformly local Lebesgue space

Md Rabiul Haque, Takayoshi Ogawa, Ryuichi Sato

1 被引用数 (Scopus)

## 抄録

We consider the local existence and the uniqueness of a weak solution of the initial boundary value problem to a convection–diffusion equation in a uniformly local function space Lr uloc,ρ(Ω), where the solution is not decaying at |x| → ∞. We show that the local existence and the uniqueness of a solution for the initial data in uniformly local Lr spaces and identify the Fujita-Weissler critical exponent for the local well-posedness found by Escobedo-Zuazua [10] is also valid for the uniformly local function class.

本文言語 English 677-697 21 Communications on Pure and Applied Analysis 19 2 https://doi.org/10.3934/cpaa.2020031 Published - 2020

• 分析
• 応用数学

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