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arXiv · 2308.12220

The blow-up rate for a loglog non-scaling invariant semilinear wave equation

Tristan Roy·Hatem Zaag
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Abstract

We consider blow-up solutions of a semilinear wave equation with a loglog perturbation of the power nonlinearity in the subconformal case, and show that the blow-up rate is given by the solution of the associated ODE which has the same blow-up time. In fact, our result shows an upper bound and a lower bound of the blow-up rate, both proportional to the blow-up solution of the associated ODE. The main difficulty comes from the fact that the PDE is not scaling invariant.

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Tristan Roy, Hatem Zaag. 2023-08-23. The blow-up rate for a loglog non-scaling invariant semilinear wave equation. https://arxiv.org/abs/2308.12220

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