Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 28, Issue 4, 2011, Pages 583-598

  Escher, Joachim ^a   Laurençot, Philippe ^b   Matioc, Bogdan Vasile ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Degenerate parabolic system; Exponential stability; Liapunov functional; Thin film; Weak solutions

Indexed keywords

MULTIPHASE FLOW; POROUS MATERIALS;

EXISTENCE AND STABILITY; EXPONENTIAL RATES; GLOBAL EXISTENCE; LIAPUNOV FUNCTIONAL; PARABOLIC SYSTEM; POROUS MEDIUM; THIN FLUID FILMS; WEAK SOLUTION;

NON NEWTONIAN FLOW;

EID: 79960641120     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2011.04.001     Document Type: Article

References (10)

1. H. Amann Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems H. Schmeisser, H. Triebel, Function Spaces, Differential Operators and Nonlinear Analysis Teubner-Texte Math. vol. 133 1993 Teubner Stuttgart/Leipzig 9 126
2. J. Escher, M. Hillairet, Ph. Laurençot, C. Walker, Global weak solutions for a degenerate parabolic system modeling the spreading of insoluble surfactant, Indiana Univ. Math. J., in press.
3. J. Escher, A.-V. Matioc, and B.-V. Matioc A generalised Rayleigh-Taylor condition for the Muskat problem arXiv:1005.2511v1
4. J. Escher, A.-V. Matioc, B.-V. Matioc, Modelling and analysis of the Muskat problem for thin fluid layers, J. Math. Fluid Mech., doi:10.1007/s00021- 011-0053-2, in press.
5. I. Fonseca, and G. Leoni Modern Methods in the Calculus of Variations: Lp Spaces Springer Monogr. Math. 2007 Springer New York
6. M. Günther, and G. Prokert A justification for the thin film approximation of Stokes flow with surface tension J. Differential Equations 245 2008 2802 2845
7. A. Lunardi Analytic Semigroups and Optimal Regularity in Parabolic Problems 1995 Birkhäuser Basel
8. B.-V. Matioc, G. Prokert, Hele-Shaw flow in thin threads: A rigorous limit result, preprint.
9. Lp (0, T; B) Ann. Mat. Pura Appl. 4 146 1987 65 96
10. J.L. Vázquez The Porous Media Equation 2007 Clarendon Press Oxford