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

The existence and uniqueness of the global solution of Cauchy problemfor a class of semi-linear heat conduction equation are discussed in this paper.With utilizing the estimation of energy and the estimation of degenerationtogether,and by the Banach fixed point theorem,the existence and uniquenessof the global solution are presented,as the initial valueφand the non-linearterm a(x)u~β|▽u|~γsatisfy some certain conditions.