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

Francesca Bucci; Matthias Eller

doi:10.5802/crmath.231

Partial differential equations, Mathematical physics

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.

Abstract
Résumé

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.

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.

Received: 2020-04-30
Revised: 2021-05-24
Accepted: 2021-06-05
Published online: 2021-09-17

Zbl

DOI: 10.5802/crmath.231

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

Author's affiliations:

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.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Francesca Bucci and Matthias Eller},
     title = {The {Cauchy{\textendash}Dirichlet} problem for the {Moore{\textendash}Gibson{\textendash}Thompson} equation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {881--903},
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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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