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.

Classification: 35B40, 35F55, 49L25

Keywords: Large-time behavior, Hamilton–Jacobi equations, Degenerate parabolic equations, Nonlinear adjoint methods, Viscosity solutions

@article{AIHPC_2015__32_1_183_0, author = {Cagnetti, Filippo and Gomes, Diogo and Mitake, Hiroyoshi and Tran, Hung V.}, title = {A new method for large time behavior of degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, publisher = {Elsevier}, volume = {32}, number = {1}, year = {2015}, pages = {183-200}, doi = {10.1016/j.anihpc.2013.10.005}, zbl = {1312.35020}, mrnumber = {3303946}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2015__32_1_183_0} }

Cagnetti, Filippo; Gomes, Diogo; Mitake, Hiroyoshi; Tran, Hung V. A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, pp. 183-200. doi : 10.1016/j.anihpc.2013.10.005. http://www.numdam.org/item/AIHPC_2015__32_1_183_0/

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