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Phragm\`en-Lindel\"of type theorems for parabolic equations on infinite graphs

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arxiv 2504.08407 v3 pith:FHPSD2B2 submitted 2025-04-11 math.AP

Stefano Biagi , Giulia Meglioli , Fabio Punzo This is my paper · ORCID
classification math.AP
keywords densityen-lindelequationsgraphsinfiniteparabolicphragmassociated
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We obtain the Phragm\`en-Lindel\"of principle on combinatorial infinite weighted graphs for the Cauchy problem associated to a certain class of parabolic equations with a variable density. We show that the hypothesis made on the density is optimal.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation

    math.AP 2026-07 conditional novelty 7.0 of 10

    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...

  2. The fractional Porous Medium Equation on graphs

    math.AP 2026-06 unverdicted novelty 6.0 of 10

    Existence of weak dual solutions to the fractional porous medium equation is shown on general infinite graphs via weighted estimates on the fractional Green function, with additional comparison and smoothing results on trees.

  3. Nonexistence results for the semilinear wave equation on graphs

    math.AP 2025-06 reject novelty 6.0 of 10

    On infinite weighted graphs, if the graph Laplacian of the distance grows slowly and suitable weighted volume growth holds, every very weak solution of the semilinear wave inequality is identically zero.

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