The Application Of Geometry Method To Partial Differential Equations With Variable Coefficients

Wave equations are one type of the most important, the earliest and most frequently researched partial differential equations.Most researchers study the stabilization of solutions for the wave equations.But since the variable coefficients wave equations can not be analyzed by this method.And the theories of fixed coefficient wave equations can not be used in variable coefficient wave equations.Many mathematicians are working in this area and have got many results. We use the Rimannian geometric method to analyze the variable coefficient wave equations with a boundary control of memory type in this paper.The organizational structure of this article:first,we introduce the basic concepts of Rie-mannian Geometry and the equations about the wave equations in this area for the used in the after demonstration. Second, we study the boundary stabilization of solutions for the coupled semilinear system with variable coefficients In the end, we study the boundary stabilization of solutions for the wave equation with a boundary control of memory type and with variable coefficients...