Electron. J. Diff. Eqns., Vol. 2007(2007), No. 82, pp. 1-15.

Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems

Stanislas Ouaro, Hamidou Toure

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.

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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
email: souaro@univ-ouaga.bf
Hamidou Toure
Laboratoire d'Analyse Mathématique des Equations (LAME), UFR.
Sciences Exactes et Appliquées, Université de Ouagadougou
03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso
email: toureh@univ-ouaga.bf

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