Remarks on the large time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations

Article type: Research Article

Authors: Mitake, Hiroyoshi^; | Tran, Hung V.

Affiliations: Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan. E-mail: mitake@hiroshima-u.ac.jp | Department of Mathematics, University of California, Berkeley, CA, USA. E-mail: tvhung@math.berkeley.edu

Note: [] Corresponding author: Hiroyoshi Mitake, Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan. E-mail: mitake@hiroshima-u.ac.jp.

Abstract: 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.

Keywords: large-time behavior, Hamilton–Jacobi equations, weakly coupled systems, ergodic problem, viscosity solutions

DOI: 10.3233/ASY-2011-1071

Journal: Asymptotic Analysis, vol. 77, no. 1-2, pp. 43-70, 2012