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

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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.
In questa nota illustreremo un risultato di esistenza per il problema di Cauchy-Dirichlet in $Q_T = \Omega \times (0, T)$ per equazioni paraboliche con parte principale degenere (del tipo "mezzi porosi") aventi un termine di grado inferiore quadratico nel gradiente. Il termine noto $f$ e il dato iniziale $u_0$ sono funzioni limitate non negative. 
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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/

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