Generalized Convergence of Solutions for Nonlinear Hamilton--Jacobi Equations with State-Constraint

Abstract

We examine the asymptotic behaviors of solutions to Hamilton-Jacobi equations with state constraints while varying the underlying domains. We establish a connection between the convergence of these solutions and the regularity of the additive eigenvalues in relation to the domains. To accomplish this, we introduce a framework based on Mather measures that enables us to compute the one-sided derivative of these additive eigenvalues under different scenarios, including first-order, second-order, and contact first-order equations. Additionally, we provide examples of how this framework can be applied to other settings.

Speaker

His current projects concentrate on the nonlinear behavior of solutions to certain types of Hamilton–Jacobi equations and their applications to the free boundary problem in some models of fluid dynamics.

https://tunguyenthaison.github.io/