A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited

Panrui Ni, Lin Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Hamilton-Jacobi equation H(x,Du)+λ(x)u=c,x∈M, where M is a connected, closed and smooth Riemannian manifold. The functions H(x,p) and λ(x) are continuous. H(x,p) is convex, coercive with respect to p, and λ(x) changes the signs. The first breakthrough to this model was achieved by Jin-Yan-Zhao [11] under the Tonelli conditions. In this paper, we consider more detailed structure of the viscosity solution set and large time behavior of the viscosity solution on the Cauchy problem. To the best of our knowledge, it is the first detailed description of the large time behavior of the HJ equations with non-monotone dependence on the unknown function.

Original languageEnglish
Pages (from-to)272-307
Number of pages36
JournalJournal of Differential Equations
Volume403
DOIs
Publication statusPublished - 15 Sept 2024

Keywords

  • Aubry-Mather theory
  • Contact Hamiltonian systems
  • Hamiltonian systems
  • Weak KAM theory

Fingerprint

Dive into the research topics of 'A nonlinear semigroup approach to Hamilton-Jacobi equations–revisited'. Together they form a unique fingerprint.

Cite this