Quasi-convex Hamilton-Jacobi equations posed on junctions: The multi-dimensional case
| Autor: | Cyril Imbert, Régis Monneau |
|---|---|
| Přispěvatelé: | Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), ANR-12-BS01-0008,HJnet,Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux(2012), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
multi-dimensional vertex test function
Applied Mathematics 010102 general mathematics Regular polygon 01 natural sciences Hamilton–Jacobi equation 010101 applied mathematics Quadratic equation Mathematics - Analysis of PDEs FOS: Mathematics Test functions for optimization multi-dimensional junctions Discrete Mathematics and Combinatorics Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Flux limiter Uniqueness 0101 mathematics Viscosity solution Hamilton-Jacobi equations Finite set Analysis Analysis of PDEs (math.AP) Mathematics 35F21 49L25 35B51 |
| Zdroj: | Discrete and Continuous Dynamical Systems-Series A Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2017, 37, pp.6405-6435. ⟨10.3934/dcds.2017278⟩ |
| ISSN: | 1078-0947 |
| DOI: | 10.3934/dcds.2017278⟩ |
| Popis: | A multi-dimensional junction is obtained by identifying the boundaries of a finite number of copies of an Euclidian half-space. The main contribution of this article is the construction of a multidimensional vertex test function G(x, y). First, such a function has to be sufficiently regular to be used as a test function in the viscosity solution theory for quasi-convex Hamilton-Jacobi equations posed on a multi-dimensional junction. Second, its gradients have to satisfy appropriate compatibility conditions in order to replace the usual quadratic pe-nalization function |x -- y| 2 in the proof of strong uniqueness (comparison principle) by the celebrated doubling variable technique. This result extends a construction the authors previously achieved in the network setting. In the multi-dimensional setting, the construction is less explicit and more delicate. Mathematical Subject Classification: 35F21, 49L25, 35B51. 28 pages. Second version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|