Pré-Publication, Document De Travail Année : 2025

Finite time blow-up for a nonlinear parabolic equation with smooth coefficients

Résumé

In this article, we consider an n-dimensional parabolic partial differential equation with a smooth coefficient term in the nonlinear gradient term. This equation was first introduced and analyzed in [E. Issoglio, On a non-linear transport-diffusion equation with distributional coefficients, Journal of Differential Equations, Volume 267, Issue 10 ( 2019)], where one of the main open questions is the possible finite-time blow-up of solutions. Here, leveraging a virial-type estimate, we provide a positive answer to this question within the framework of smooth solutions.

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Dates et versions

hal-04930914 , version 1 (05-02-2025)
hal-04930914 , version 2 (20-03-2025)

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  • HAL Id : hal-04930914 , version 2

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Oscar Jarrin, Gaston Vergara-Hermosilla. Finite time blow-up for a nonlinear parabolic equation with smooth coefficients. 2025. ⟨hal-04930914v2⟩

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