A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians

Filippo Cagnetti; Diogo A. Gomes; Hiroyoshi Mitake; Hung V. Tran

doi:10.1016/j.anihpc.2013.10.005

A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians

Filippo Cagnetti, Diogo A. Gomes, Hiroyoshi Mitake, Hung V. Tran

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We investigate large-time asymptotics for viscous Hamilton-Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.

Original language	English (US)
Pages (from-to)	183-200
Number of pages	18
Journal	Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Volume	32
Issue number	1
DOIs	https://doi.org/10.1016/j.anihpc.2013.10.005
State	Published - Jan 2015

ASJC Scopus subject areas

Mathematical Physics
Analysis

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10.1016/j.anihpc.2013.10.005

https://repository.kaust.edu.sa/bitstream/10754/346767/1/1-s2.0-S0294144913001303-main.pdf

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AU - Tran, Hung V.

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AB - We investigate large-time asymptotics for viscous Hamilton-Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.

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A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians

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