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Comptes Rendus. Mathématique
Partial differential equations, Mathematical physics
The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 881-903.

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.

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DOI: 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.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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