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.

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{\textendash}Jacobi} equations with convex {Hamiltonians}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {183--200}, publisher = {Elsevier}, volume = {32}, number = {1}, year = {2015}, doi = {10.1016/j.anihpc.2013.10.005}, zbl = {1312.35020}, mrnumber = {3303946}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2013.10.005/} }

TY - JOUR AU - Cagnetti, Filippo AU - Gomes, Diogo AU - Mitake, Hiroyoshi AU - Tran, Hung V. TI - A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 DA - 2015/// SP - 183 EP - 200 VL - 32 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2013.10.005/ UR - https://zbmath.org/?q=an%3A1312.35020 UR - https://www.ams.org/mathscinet-getitem?mr=3303946 UR - https://doi.org/10.1016/j.anihpc.2013.10.005 DO - 10.1016/j.anihpc.2013.10.005 LA - en ID - AIHPC_2015__32_1_183_0 ER -

%0 Journal Article %A Cagnetti, Filippo %A Gomes, Diogo %A Mitake, Hiroyoshi %A Tran, Hung V. %T A new method for large time behavior of degenerate viscous Hamilton–Jacobi equations with convex Hamiltonians %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 183-200 %V 32 %N 1 %I Elsevier %U https://doi.org/10.1016/j.anihpc.2013.10.005 %R 10.1016/j.anihpc.2013.10.005 %G en %F 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://archive.numdam.org/articles/10.1016/j.anihpc.2013.10.005/

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