The Existence Of Global Solutions For The Initial-Boundary Value Problem Of The Parabolic Equation

In this paper,we study the initial boundary value problem of nonlinear parabolic equation.Ω(?) Rⁿ is a bounded domain. And the existence and nonexistence of global solutions are established.A family of potential wells that we defined combined with the Galerkin method soloved the existence problem of the weak solutions and regular solutions, and the existence terms of the weak solutions and regular solutions were obtained. On the bases of these research vacuum isolating property of the solutions of the equations were obtained .That means that all solutions of the equations may be in a small ball or out of a large ball of W₀^l,p (Ω)space. At last by using potential well method we studied the nonlinear parabolic equation with critical initial conditions, and obtain some new existence theorems of global solutions.