Well-posedness of a Debye type system endowed with a full wave equation

被引：1
|
作者：
Heibig, Arnaud [1 ]
机构：
[1] Univ Lyon, Inst Camille Jordan, INSA Lyon, Bat Leonard de Vinci 401,21 Ave Jean Capelle, F-69621 Villeurbanne, France
来源：
APPLIED MATHEMATICS LETTERS | 2018年 / 81卷
关键词：
Transport-diffusion equation; Wave equation; Debye system; Chemin-Lerner spaces; Gagliardo-Nirenberg inequalities; TIME BEHAVIOR; EXISTENCE;
D O I：
10.1016/j.aml.2018.01.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove well-posedness for a transport-diffusion problem coupled with a wave equation for the potential. We assume that the initial data are small. A bilinear form in the spirit of Kato's proof for the Navier-Stokes equations is used, coupled with suitable estimates in Chemin-Lerner spaces. In the one dimensional case, we get well-posedness for arbitrarily large initial data by using Gagliardo-Nirenberg inequalities. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码：27 / 34
页数：8
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