Some Results on the Large Time Behavior of Weakly Coupled Systems of First-order Hamilton-jacobi Equations
نویسنده
چکیده
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. The large time behavior for systems of Hamilton-Jacobi equations have been obtained by Camilli-Loreti-Ley and the author (2012) and Mitake-Tran (2012) under quite strict conditions. In this work, we use a PDE approach to extend the convergence result proved by Barles-Souganidis (2000) in the scalar case. This general result permits us to treat lot of general cases, for instance, systems with nonconvex Hamiltonians and systems with strictly convex Hamiltonians. We also obtain some other convergence results under different assumptions, these results give a clearer view on the large time behavior for systems of Hamilton-Jacobi equations.
منابع مشابه
Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
Abstract. We show a large time behavior result for class of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. We use a PDE approach to extend the convergence result proved by Namah and Roquejoffre (1999) in the scalar case. Our proof is based on new comparison, existence and regularity results for systems. An interpretation of the solution of the system in...
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