Higher Order Dissipative-Dispersive System and Application (Journal of Partial Differential Equations, 2020)
In this paper, a generalized nonlinear dissipative and dispersive equationwith time and space-dependent coefficients is considered. We show that the control ofthe higher order term is possible by using an adequate weight function to define theenergy. The existence and uniqueness of solutions are obtained via a Picard iterativemethod. As an application to this general Theorem, we prove the well-posedness ofthe Camassa-Holm type equation.
Keywords: Cauchy problem; Euler system; dispersive wave equation; Camassa-Holm equation.