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A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians
Journal article   Open access  Peer reviewed

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

Filippo Cagnetti, Diogo Gomes, Hiroyoshi Mitake and Hung V. Tran
Annales de l'Institut Henri Poincaré. Analyse non linéaire, Vol.32(1), pp.183-200
01/01/2015
DOI: https://doi.org/10.1016/j.anihpc.2013.10.005

Abstract

Degenerate parabolic equations Hamilton–Jacobi equations Large-time behavior Nonlinear adjoint methods Viscosity solutions
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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https://doi.org/10.1016/j.anihpc.2013.10.005View
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