Existence And Uniqueness For Global Solution Of Cauchy Problem Of A Class Of Nonlinear Heat Conduction Equation

The existence and uniqueness for the global solution of Cauchy problem of a class of non-linear heat conduction equations are discussed in this paper. With utilizing the estimation of energy and the estimation of degeneration together,and according to Banach fixed point theorem,the existence and uniqueness of the global solution are presented,when the initial value φ and the non-linear item V(x)u + u~p satisfy some certain conditions.