The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation

Francesca Bucci; Matthias Eller

doi:10.5802/crmath.231

Équations aux dérivées partielles, Physique mathématique

The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation

Francesca Bucci ¹ ; Matthias Eller ²

¹ Università degli Studi di Firenze, Dipartimento di Matematica e Informatica, Via S. Marta 3, 50139 Firenze, Italy.
² Georgetown University, Department of Mathematics and Statistics, Georgetown 360, 37th and O Streets NW, Washington DC 20057, USA.

Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 881-903.

Résumé
Abstract

On analyse le problème de Cauchy–Dirichlet pour l’équation de Moore–Gibson–Thompson avec des données non-homogènes. Deux méthodes sont considérées : la théorie des équations hyperboliques et la théorie des semi-groupes d’opérateurs. Il s’agit d’un problème hyperbolique mixte avec une frontière spatiale caractéristique. Par conséquent, les résultats de régularité présentent certaines lacunes par rapport au cas non caractéristique.

The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation is analyzed. With the focus on non-homogeneous boundary data, two approaches are offered: one is based on the theory of hyperbolic equations, while the other one uses the theory of operator semigroups. This is a mixed hyperbolic problem with a characteristic spatial boundary. Hence, the regularity results exhibit some deficiencies when compared with the non-characteristic case.

Reçu le : 2020-04-30
Révisé le : 2021-05-24
Accepté le : 2021-06-05
Publié le : 2021-09-17

Zbl

DOI : 10.5802/crmath.231

Classification : 35B65, 35L35, 35L50, 35R09

Affiliations des auteurs :

Francesca Bucci ¹ ; Matthias Eller ²

¹ Università degli Studi di Firenze, Dipartimento di Matematica e Informatica, Via S. Marta 3, 50139 Firenze, Italy.
² Georgetown University, Department of Mathematics and Statistics, Georgetown 360, 37th and O Streets NW, Washington DC 20057, USA.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {The {Cauchy{\textendash}Dirichlet} problem for the {Moore{\textendash}Gibson{\textendash}Thompson} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {881--903},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {7},
     year = {2021},
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     language = {en},
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Francesca Bucci; Matthias Eller. The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 881-903. doi : 10.5802/crmath.231. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.231/

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