Dissipative Solutions Of Generalized Two - Component Shallow Water Wave Equations

This paper,we focus on the system of the generalized two component for shallow water waves of moderate amplitude here,u is the horizontal of of the fluid,φ is the free surface elevation.By introducing a new set of independent and dependent variables, the system is transformed into a semilinear system in an L∞ and the variables will be rewrit-ten space .In this way,the partial differential system with the Cauchy problem can be replace by the ordinary differential system with the Cauchy problem.As follow,the ordinary differential system is endowed with the norm and we give the proof to the total energy.Finally, we set three theorem and proof with the theorem.This paper is organized as follow.Chaper l,we introduce some background knowledge.Chaper 2,By introducing a new set of independent and dependent variables,the system is transformed into a semilinear system in an L∞ and the variables will be rewritten space.we introduce preliminaries with the system.Chaper 3,we set three theorem and proof with the theorem and we focus on the main result.