Well-posedness of a Debye type system endowed with a full wave equation. (July 2018)

• Record Type: Journal Article
• Authors: Heibig, Arnaud
• Is Part Of: Applied mathematics letters. Volume 81(2018)
• Page Start: 27
• Page End: 34
• Publication Date: 2018-07
• Subjects: Transport-diffusion equation -- Wave equation -- Debye system -- Chemin–Lerner spaces -- Gagliardo–Nirenberg inequalities; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.01.015
• Languages: English
• ISSNs: 0893-9659

Abstract

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.