Gabriele Grillo

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math.AP2024

Blow-up and global existence for semilinear parabolic equations on infinite graphs

Gabriele Grillo, Giulia Meglioli, Fabio Punzo

We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f (u)$ …

math.AP2012

Sharp short and long time $L^{\infty}$ bounds for solutions to porous media equations with Neumann boundary conditions

Gabriele Grillo, Matteo Muratori

We study a class of nonlinear diffusion equations whose model is the classical porous media equation on domains $Ω \subseteq R^{N}$ , $N \geq 3$ , with homogeneous Neumann boundar…

math.AP2012

Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities

Gabriele Grillo, Matteo Muratori, Maria Michaela Porzio

We study weighted porous media equations on domains $Ω \subseteq R^{N}$ , either with Dirichlet or with Neumann homogeneous boundary conditions when $Ω \neq = R^{N}$ . Exi…

Blow-up and global existence for semilinear parabolic equations on infinite graphs

Sharp short and long time L∞ bounds for solutions to porous media equations with Neumann boundary conditions

Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincaré inequalities

Sharp short and long time $L^{\infty}$ bounds for solutions to porous media equations with Neumann boundary conditions