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Porous Medium Type Equations with a Quadratic Gradient Term

Daniela Giachetti; Giulia Maroscia — 2007

Bollettino dell'Unione Matematica Italiana

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.

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