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 (Commun. Partial. Differ. Equ. 24(5-6):883-893, 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 terms of an optimal control problem with switching is given. © 2011 Springer Basel AG.
Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations / Camilli, Fabio; Olivier, Ley; Loreti, Paola; Vinh Duc, Nguyen. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 19:6(2012), pp. 719-749. [10.1007/s00030-011-0149-7]
Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations
CAMILLI, FABIO;LORETI, Paola;
2012
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 (Commun. Partial. Differ. Equ. 24(5-6):883-893, 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 terms of an optimal control problem with switching is given. © 2011 Springer Basel AG.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
