The Initial Boundary Problem Of The Semilinear Heat Equation With Two Temperatures

In this paper we study the initial boundary problem for semilinear heat equations with two temperaturesthe existence and uniqueness of the global W^2,2 , W^2,p(p>2) ,and W^k,p (k≥1,1 < p <∞) solutions are stteined.First we establish the existence and uniqueness of global W^2,2 solutions.Then by the method of successive smoothingand using parameters variation method of Ordinary differential equation,we obtain the existence and uniqueness of global W^2,p(p > 2) solutions.At last bysmoothing on k .we obtain the existence and uniqueness of global W^k,p (k≥1,1 < p <∞) solutions.