Full paper in PDF format:
$%S. Ouaro, Uniqueness of entropy solutions of nonlinear elliptic-parabolic-hyperbolic problems in one dimension space, Rev. Mat. Complut. 22 (2009), no. 1, 7–36.%$

Uniqueness of Entropy Solutions of Nonlinear Elliptic-Parabolic-Hyperbolic Problems in One Dimension Space

Stanislas OUARO

Laboratoire d’Analyse Mathématique des Equations (LAME)
UFR. Sciences Exactes et Appliquées
Université de Ouagadougou
03 BP 7021 Ouaga 03
Ouagadougou — Burkina Faso
souaro@univ-ouaga.bf

Received: November 20, 2006
Accepted: November 19, 2007

ABSTRACT

We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form $b(u)t- a(u,φ(u)x)x = f$ with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an $1 L$ -contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data.

Key words: elliptic, parabolic, hyperbolic, weak solution, entropy solution, $L1$ -contraction principle.
2000 Mathematics Subject Classification: 35K65, 35L65.