Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 46, pp. 1-31.

Title: On uniqueness and existence of entropy
       solutions of weakly coupled systems
       of nonlinear degenerate parabolic equations

Authors: Helge Holden (Norwegian Univ. of Sci. & Tech., Norway)
         Kenneth H. Karlsen (Univ. of Bergen, Norway)
	 Nils H. Risebro (Univ. of Oslo, Norway)

Abstract: 
  We prove existence and uniqueness of entropy solutions for
  the Cauchy problem of weakly coupled systems  of nonlinear
  degenerate parabolic equations.  We prove existence of  an
  entropy solution by demonstrating that the  Engquist-Osher
  finite difference scheme is  convergent and that any limit
  function satisfies  the entropy condition. The convergence
  proof is based on  deriving a series of a priori estimates
  and using a general $L^p$ compactness criterion.
  The uniqueness proof is an adaption of Kruzkov's
  ``doubling of variables'' proof. We also present a numerical
  example motivated by biodegradation in porous media.
 
Submitted October 18, 2002. Published April 22, 2003.
Math Subject Classifications: 35K65, 65M12, 35L65.
Key Words: Nonlinear degenerate parabolic equations; 
           weakly coupled systems; entropy solution; uniqueness;
           existence; finite difference method