Geodesic
Porous Medium Type Equations with a Quadratic Gradient Term
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 753-759

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We show an existence result for the Cauchy-Dirichlet problem in $Q_T = \Omega \times (0, T)$ for parabolic equations with degenerate principal part (of porous medium type) with a lower order term having a quadratic growth with respect to the gradient. The right hand side of the equation $f$ and the initial datum $u_0$ are bounded nonnegative functions. 
@article{BUMI_2007_8_10B_3_a19,
     author = {Giachetti, Daniela and Maroscia, Giulia},
     title = {Porous {Medium} {Type} {Equations} with a {Quadratic} {Gradient} {Term}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {753--759},
     publisher = {mathdoc},
     volume = {Ser. 8, 10B},
     number = {3},
     year = {2007},
     zbl = {1177.35124},
     mrnumber = {2351544},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a19/}
}
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Giachetti, Daniela; Maroscia, Giulia. Porous Medium Type Equations with a Quadratic Gradient Term. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 753-759. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a19/