Geodesic
On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general $L^p$ compactness criterion. The uniqueness proof is an adaption of Kruzkov's "doubling of variables" proof. We also present a numerical example motivated by biodegradation in porous media.
Classification : 35K65, 65M12, 35L65
Keywords: nonlinear degenerate parabolic equations, weakly coupled systems, entropy solution, uniqueness, existence 
@article{EJDE_2003__2003__a49,
     author = {Holden, Helge and Karlsen, Kenneth H. and Risebro, Nils H.},
     title = {On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a49/}
}
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Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H. On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a49/