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Article Dans Une Revue Applied Mathematics Letters Année : 2018

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

Résumé

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.
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Dates et versions

hal-01840160 , version 1 (16-07-2018)

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Arnaud Heibig. Well-posedness of a Debye type system endowed with a full wave equation. Applied Mathematics Letters, 2018, 81, pp.27-34. ⟨10.1016/j.aml.2018.01.015⟩. ⟨hal-01840160⟩
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