Year: 2024
Type: article
Abstract: In this paper, we show how to extend the twin blow-up method recently developped by the authors (Comptes Rendus. Math., 2024), in order to obtain a new comparison principle for an evolution coercive Hamilton–Jacobi equation posed in a domain of an Euclidian space of any dimension and supplemented with a boundary condition. The method allows dealing with the case where tangential variables and the variable corresponding to the normal gradient of the solution are strongly coupled at the boundary. We elaborate on a method introduced by Lions and Souganidis (Atti Accad. Naz. Lincei, 2017). Their argument relies on a single blow-up procedure after rescaling the semi-solutions to be compared while two simultaneous blow-ups are performed in this work, one for each variable of the classical doubling variable technique. A one-sided Lipschitz estimate satisfied by a combination of the two blow-up limits plays a key role.
DOI: 10.1051/cocv/2024090
Authors: Nicolas Forcadel, Cyril Imbert, Régis Monneau
Institutions: Laboratoire de Mathématiques de l'INSA de Rouen, Institut National des Sciences Appliquées Rouen Normandie, Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, École Normale Supérieure - PSL, Département de mathématiques et applications, Centre de Recherche en Mathématiques de la Décision, CERMICS
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid:
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4405259062