Existence of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form

摘要

In this paper,we discuss the existence of weak solutions to the initial and boundary value problem of a class of nonlinear degenerate parabolic equations in non-divergence form.Applying the method of parabolic regularization,we prove the existence of weak solutions to the problem.By carefully analyzing the approximate solutions to the problem,we make a series of estimates to the solutions and prove the weak convergence of the approximation solution sequence.Finally we testify the existence of weak solutions to the problem.