Existence And Uniqueness For Global Solution Of Cauchy Problem Of A Class Of Nonlinear Wave Equation And The Verhulst PDE Model

The global existence and uniqueness of solution to the equations are discussedin this paper. In the first part, with utilizing the estimation of energy and theestimation of degeneration together, and according to Banach fixed point theo-rem. the existence and uniqueness of the global solution are presented When theinitial value f(x),g(x) and the dimensionn,p satisfy some certain conditions.Also in the second part, with analyzing the properties of an operator , the globalexistence and uniqueness, the regularity and the dependence on the initial valuesof the solution about this model are presented.