Doubly Non-linear Elliptic-parabolic Equations by Rothe's Method
Jaouad Igbida *
Department of Mathematics, CRMEF, Centre Regional des Metiers de l'Education et de la Formation El Jadida, Morocco.
Abderrahmane El Hachimi
Department of Mathematics, Faculté des Sciences, Universite Mohammed V- Agdal Rabat, Morocco.
Ahmed Jamea
Department of Mathematics, CRMEF, Centre Regional des Metiers de l'Education et de la Formation El Jadida, Morocco.
Abassi Asmaa
Department of Mathematics, Faculté des Sciences, Universite Chouaib Doukkali El Jadida, Morocco.
*Author to whom correspondence should be addressed.
Abstract
This work is devoted to study a doubly non linear elliptic-parabolic problem with quadratic gradient term by Rothe's method. We investigate the long time behavior of the solution to the discrete problem and prove the existence of compact global attractor. Our method relays on semi-discretization with respect to the time variable.
Keywords: Semi-discretization, Euler forward scheme, attractor, parabolic, elliptic, existence, uniqu-eness, stability.