On infinite weighted graphs, porous-medium solutions extinguish in finite time in the fast-diffusion range m < 2/ν, smooth into every ℓ^q for m > 2/ν, and satisfy an exact mass balance under stochastic completeness at infinity.
Global properties of Dirichlet forms in terms of Green’s formula
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The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation
On infinite weighted graphs, porous-medium solutions extinguish in finite time in the fast-diffusion range m < 2/ν, smooth into every ℓ^q for m > 2/ν, and satisfy an exact mass balance under stochastic completeness at infinity.