Existence Of Solutions To A Quasilinear Parabolic Equation With Degenerated Coefficients

In this thesis, we mainly study existence of solutions of quasilinear parabolic equations with coefficient degeneracy. First, we discrete the problem into elliptic problems by using the the Rothe method. Secondly, we prove the existence of solution to the elliptic problem with the variational method. And then we construct two types of approximation solutions, prove a priori estimates and apply weak convergence method to prove the existence of solutions to some regularization problems. Finally, using the parabolic regularization method and a priori estimates, we give the proof of existence of solution of the parabolic problem discussed in this thesis.