Higher Order Dissipative-Dispersive System and Application

Abstract

In this paper, a generalized nonlinear dissipative and dispersive equation with time and space-dependent coefficients is considered. We show that the control of the higher order term is possible by using an adequate weight function to define the energy. The existence and uniqueness of solutions are obtained via a Picard iterative method. As an application to this general Theorem, we prove the well-posedness of the Camassa-Holm type equation.