Existence and uniqueness of the solutions of continuous nonlinear 2D Roesser models: The locally Lipschitz continuous case

Abstract

This paper investigates the existence and uniqueness of the solution of the nonlinear continuous 2D Roesser model. We first remind the reader of the results obtained in the globally Lipschitz continuous case where a global solution is always to be found. Then we investigate the more general case which could be applied in more situations: when the function describing the system is only supposed locally Lipschitz continuous. Since in this case the solution will be defined only locally, the question of whether we can extend the solutions or not is answered.