Global Solutions Existence For The Voscous Dffusion Equation

In this paper, we study a viscous diffusion equationwhereΩis a bounded domain with smooth boundary in R~n,ρ≥0 the viscosity coefficient, A(s) a continuously differentiable function on R with A'(s)≥0, B(s) =φ(A(s)), andφ(s)a locally Lipschitz continuous vector-valued function. By using eigenfunction method and integral estimate method we obtain the global existence and uniqueness of solutions, and when the nonlinear terms of the equation satisfy some other conditions the solutions blow up in finite time.