Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 82, pp. 1-15.
Title: Uniqueness of entropy solutions to nonlinear
elliptic-parabolic problems
Authors: Stanislas Ouaro (Univ. de Ouagadougou, Burkina Faso)
Hamidou Toure (Univ. de Ouagadougou, Burkina Faso)
Abstract:
We study the Cauchy problem associated with the nonlinear
elliptic - parabolic equation
$$
b(u)_{t}-a(u,\varphi(u)_x)_x=f.
$$
We prove an $L^{1}$-contraction principle and hence the uniqueness of
entropy solutions, under rather general assumptions on the data.
Submitted November 11, 2005. Published May 29, 2007.
Math Subject Classifications: 35K65, 35L65.
Key Words: Elliptic; parabolic; degenerate; weak solution;
entropy solution; L1-contraction principle.