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

页码：27 / 34

页数：8

共 10 条

[1]

Bahouri Hajer, 2011, FOURIER ANAL NONLINE, V343

[2] THE DEBYE SYSTEM - EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS [J].