Glasnik Matematicki, Vol. 55, No. 1 (2020), 93-99.
UNIQUENESS OF SOLUTION OF A HETEROGENEOUS EVOLUTION DAM PROBLEM ASSOCIATED WITH A COMPRESSIBLE FLUID FLOW THROUGH A RECTANGULAR POROUS MEDIUM
Elmehdi Zaouche
Department of Mathematics, University of EL Oued, B. P. 789 El Oued 39000, Labo. Part. Diff. Eq. & Hist. Maths,
Ecole Normale Supérieure, 16050 Vieux-Kouba Algiers, Algeria
e-mail: elmehdi-zaouche@univ-eloued.dz
Abstract.
This paper is concerned with the uniqueness of a weak
solution of an evolution dam problem arising in a compressible
fluid flow through a two-dimensional, rectangular, and heterogeneous
porous medium. Our problem is associated with the equation
a(x1)(ux2+χ)x2-(u+χ)t=0. The technique we use is
based on a transformation of the weak form of this equation into a
similar one that enables us to argue as in [12].
2010 Mathematics Subject Classification. 35A02, 35B35, 76S05
Key words and phrases. Heterogeneous evolution dam problem, compressible fluid
flow, rectangular porous medium, uniqueness
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https://doi.org/10.3336/gm.55.1.08
References:
- S. J. Alvarez and R. Oujja,
On the uniqueness of the solution of an evolution free
boundary problem in theory of lubrication, Nonlinear Anal.
54 (2003), 845-872.
MathSciNet
CrossRef
- M. Bousselsal, A. Lyaghfouri and E. Zaouche,
On the existence of a solution of a class of non-stationary
free boundary problems, Glas. Mat. Ser. III 53(73) (2018),
449-475.
MathSciNet
CrossRef
- J. Carrillo,
On the uniqueness of the solution of the evolution dam
problem, Nonlinear Anal. 22 (1994), 573-607.
MathSciNet
CrossRef
- J. Carrillo and G. Gilardi,
La vitesse de propagation dans le problème de la digue,
Ann. Fac. Sci. Toulouse Math. (5) 11 (1990), 7-28.
MathSciNet
CrossRef
- E. DiBenedetto and A. Friedam,
Periodic behaviour for the evolutionary dam problem and
related free boundary problems, Comm. Partial Differential
Equations 11 (1986), 1297-1377.
MathSciNet
CrossRef
- G. Gilardi,
A new approach to evolution free boundary problems, Comm.
Partial Differential Equations 4 (1979), 1099-1123;
5 (1980), 983-984.
MathSciNet
MathSciNet
CrossRef
- D. Gilbarg and N. S. Trudinger,
Elliptic partial differential equations of second order,
Springer, New York, 1983.
MathSciNet
CrossRef
- A. Lyaghfouri,
The evolution dam problem for nonlinear Darcy's law and
Dirichlet boundary conditions, Portugal. Math. 56 (1999),
1-37.
MathSciNet
- A. Lyaghfouri and E. Zaouche,
Lp-continuity of solutions to parabolic free boundary
problems, Electron. J. Differ. Equations 2015, No. 184, 9 pp.
MathSciNet
- A. Lyaghfouri and E. Zaouche,
Uniqueness of solution of the unsteady filtration problem in
heterogeneous porous media, Rev. R. Acad. Cienc. Exactas
Fis. Nat. Ser. A Math. RACSAM 112 (2018), 89-102.
MathSciNet
CrossRef
- A. Torelli,
Existence and uniqueness of the solution of a non steady
free boundary problem, Boll. Un. Mat. Ital. B (5) 14
(1977), 423-466.
MathSciNet
- E. Zaouche,
Uniqueness of solution in a rectangular domain of an
evolution dam problem with heterogeneous coefficients,
Electron. J. Differ. Equations 2018, No. 169, 17 pp.
MathSciNet
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