English

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

Analysis of PDEs 2018-01-26 v3

Abstract

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.

Keywords

Cite

@article{arxiv.1711.06603,
  title  = {Well-posedness of a Debye type system endowed with a full wave equation},
  author = {Arnaud Heibig},
  journal= {arXiv preprint arXiv:1711.06603},
  year   = {2018}
}