Blow-up on metric graphs and Riemannian manifolds

Fabio Punzo; Alberto Tesei

doi:10.3934/dcdsb.2023016

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2023, Volume 28, Issue 12: 6362-6392. Doi: 10.3934/dcdsb.2023016

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Blow-up on metric graphs and Riemannian manifolds

Fabio Punzo^1, and
Alberto Tesei^2,3, ,

1.
Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy
2.
Dipartimento di Matematica "G. Castelnuovo", Università Sapienza di Roma, P.le A. Moro 5, I-00185 Roma, Italy
3.
Istituto per le Applicazioni del Calcolo "M. Picone", CNR, Via dei Taurini 19, I-00185 Roma, Italy

^*Corresponding author: Alberto Tesei
^*Corresponding author: Alberto Tesei

Received: April 2022

Revised: October 2022

Early access: February 9, 2023

Published online: February 9, 2023

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Abstract

We study blow-up versus global existence of solutions to a model semilinear parabolic equation in metric measure spaces. Applications to metric graphs and Riemannian manifolds are considered, pointing out the occurrence of the Fujita phenomenon.

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Mathematics Subject Classification: 35B44, 35K55, 35R01, 35R02.

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References

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