Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation - Université Claude Bernard Lyon 1 Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation

Résumé

In quantitative genetics, viscosity solutions of Hamilton-Jacobi equations appear naturally in the asymptotic limit of selection-mutation models when the population variance vanishes. They have to be solved together with an unknown function I(t) that arises as the counterpart of a non-negativity constraint on the solution at each time. Although the uniqueness of viscosity solutions is known for many variants of Hamilton-Jacobi equations, the uniqueness for this particular type of constrained problem was not resolved, except in a few particular cases. Here, we provide a general answer to the uniqueness problem, based on three main assumptions: convexity of the Hamiltonian function H(I, x, p) with respect to p, monotonicity of H with respect to I, and BV regularity of I(t).
Fichier principal
Vignette du fichier
Calvez-Lam-uniqueness-constrained-HJ-18-09-12-HAL.pdf (358.97 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01873119 , version 1 (12-09-2018)

Identifiants

Citer

Vincent Calvez, King-Yeung Lam. Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation. 2018. ⟨hal-01873119v1⟩
198 Consultations
140 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More