Second Order Singular Parabolic Equation With Initial Boundary Value Problems Existence, Uniqueness And Asymptotic Estimates

This paper contains two parts. First, by applying parabolic regularization method and the sub-super solutions method, we are concerned with the existence, uniqueness and estimates of solutions to the initial and boundary value problemsin a smooth bounded domainΩ(?)R^N.Under the assumptions on b, h andφ, some existence results are obtained. We also discuss the estimates of solutions in the sense of L²(0,T;W₀^1,2(Ω))∩L^∞(0,T;L²(Ω)) norms. Moreover, we give the uniqueness of solutions for two kinds of special problems.Second, under the assumptions on f and b, by applying Karamata regular variation theory and perturbation method and constructing comparison functions, we derive the boundary behavior of solutions to boundary blow-up nonlinear elliptic problemsThis is a more generalized stable form of the above singular parabolic problem with initial and boundary values.