Équations aux dérivées partielles, Physique mathématique
The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation
Comptes Rendus. Mathématique, Tome 359 (2021) no. 7, pp. 881-903.

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.

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DOI : https://doi.org/10.5802/crmath.231
Classification : 35B65,  35L35,  35L50,  35R09
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.
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Francesca Bucci; Matthias Eller. The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation. Comptes Rendus. Mathématique, Tome 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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