A class of fourth-order parabolic systems with time dependent coefficients with blow-up solutions

Duzgun, Fatma Gamze;Marras, Monica

;Vernier-Piro, Stella

2026-01-01

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Abstract

This paper deals with a class of initial-boundary value problems for nonlinear fourth-order parabolic systems with time dependent coefficients in a bounded domain. We establish conditions on the shape of the spatial domain and on data sufficient to guarantee that the solution blows up in finite time t *, deriving an upper bound for t *. Moreover, by introducing suitable conditions on the source terms, we obtain a lifespan of the solution, i.e. a time interval [0, T], where the solution exists and remains bounded, by deriving a lower bound T of the blow-up time t *.