IJPAM: Volume 25, No. 2 (2005)

ON SOME NONLINEAR ELLIPTIC-PARABOLIC
EQUATIONS OF SECOND ORDER

Stanislas Ouaro$^1$, Hamidou Toure$^2$
$^{1,2}$Laboratoire d'Analyse Mathématique des Equations (LAME)
UFR. SEA, University of Ouagadougou
P.O. Box 7021, Ouaga 03, Ouagadougou, BURKINA FASO
$^1$e-mail: souaro@univ-ouaga.bf
$^2$e-mail: toureh@univ-ouaga.bf


In honour of Professor Phillipe Benilan.


Abstract.We study a nonlinear elliptic-parabolic PDE in one dimensional space with the form: $b(u)_{t}-a(u,\varphi(u)_{x})_{x}=f$. Using the nonlinear semi-groups theory in Banach spaces, we establish existence and uniqueness of mild solutions of the associated Cauchy problem under general assumptions on the data. We prove with additional assumptions, that mild solutions are entropy solutions.

Received: October 18, 2005

AMS Subject Classification: 35K65, 35L65

Key Words and Phrases: elliptic, parabolic, weak solution, entropy solution, mild solution, semi-group

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 2