Well-posedness of a Debye type system endowed with a full wave equation
| Autor: | Arnaud Heibig |
|---|---|
| Přispěvatelé: | Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2018 |
| Předmět: |
Gagliardo-Nirenberg inequalities
Mathematics::Analysis of PDEs Bilinear form Type (model theory) 01 natural sciences symbols.namesake Mathematics - Analysis of PDEs Full wave FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics Debye 35Q Applied Mathematics Debye system 010102 general mathematics Mathematical analysis Transport-diffusion equation 010101 applied mathematics Arbitrarily large Chemin-Lerner spaces symbols wave equation Well posedness Analysis of PDEs (math.AP) |
| Zdroj: | Applied Mathematics Letters Applied Mathematics Letters, Elsevier, 2018, 81, pp.27-34. ⟨10.1016/j.aml.2018.01.015⟩ |
| ISSN: | 0893-9659 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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