Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 4, Pages 395-402
doi:10.1155/JIA.2005.395

The Dirichlet problem for a class of nonlinear degenerate parabolic equations

Pigong Han

 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
Received 6 June 2003; Revised 21 October 2003

Abstract

We study the first boundary value problem for a class of nonlinear degenerate parabolic equations −∂u/∂t=div(A→(∇u)). We first consider its regularized problem and establish some estimates. Based on these estimates, we prove the existence and uniqueness of the generalized solutions in BV space.