Remarks on the large time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton-Jacobi equations. (English) Zbl 1241.35020

Mitake, Hiroyoshi; Tran, Hung V.

Asymptotic Anal. 77, No. 1-2, 43-70 (2012).

Summary: We investigate the large-time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton-Jacobi equations on the \(n\)-dimensional torus. We establish a convergence result to asymptotic solutions as time goes to infinity under rather restricted assumptions.

MSC:

35B40	Asymptotic behavior of solutions to PDEs
35D40	Viscosity solutions to PDEs
35F21	Hamilton-Jacobi equations

Keywords:

ergodic problem; \(n\)-dimensional torus