Existence of Bounded Weak Solutions for a Class of Nonlinear Degenerate Parabolic Equations

This paper deals with a class of nonlinear degenerate parabolic equations whose main operators goes to zero as the solution tends to infinity,when the solution of u tends to infinity, the diffusion phenomenon disappears. Using a priori estimation method and classical compactness theory, we obtain the L^∞ estimates for the solutions, and then prove the existence of bounded weak solutions to such problems.