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A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations with convex Hamiltonians. (English) Zbl 1312.35020
Summary: 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.

##### MSC:
 35B40 Asymptotic behavior of solutions to PDEs 35F55 Initial value problems for systems of nonlinear first-order PDEs 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 35F21 Hamilton-Jacobi equations 35K65 Degenerate parabolic equations 35D40 Viscosity solutions to PDEs
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