Geodesic
Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems
Electronic Journal of Differential Equations, Tome 2007 (2007).

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

Summary: We study the Cauchy problem associated with the nonlinear elliptic - parabolic equation $$ b(u)_{t}-a(u,\varphi(u)_x)_x=f. $$ We prove an $L^{1}$-contraction principle and hence the uniqueness of entropy solutions, under rather general assumptions on the data.
Classification : 35K65, 35L65
Keywords: elliptic, parabolic, degenerate, weak solution, entropy solution, L1-contraction principle 
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     author = {Ouaro, Stanislas and Toure, Hamidou},
     title = {Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a92/}
}
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Ouaro, Stanislas; Toure, Hamidou. Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a92/