Pré-Publication, Document De Travail Année : 2026

Regularity and singularity of the blow-up curve for a wave equation with a derivative nonlinearity and a scale-invariant damping

Ahmed Bchatnia
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Makram Hamouda
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Firas Kaabi
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Takiko Sasaki
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Résumé

In this article, we investigate the blow-up behavior of solutions to the one-dimensional damped nonlinear wave equation, namely

Under the assumption of sufficiently large and smooth initial data, we establish that the blow-up curve is continuously differentiable (C 1). A key step in our analysis involves the characterization of the blow-up profile of the solution. The proof relies on transforming the equation into a first-order system and adapting the techniques of Sasaki in [23, 24] which have elegantly extended the method of Caffarelli and Friedman [2] to nonlinear wave equations with time derivative nonlinearity, but without the scale-invariant term (µ = 0).

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Dates et versions

hal-05581817 , version 1 (06-04-2026)

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  • HAL Id : hal-05581817 , version 1

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Ahmed Bchatnia, Makram Hamouda, Firas Kaabi, Takiko Sasaki, Hatem Zaag. Regularity and singularity of the blow-up curve for a wave equation with a derivative nonlinearity and a scale-invariant damping. 2026. ⟨hal-05581817⟩
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