The blow-up rate for strongly perturbed semilinear wave equations in the conformal regime without a radial assumption

Mohamed-Ali Hamza

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arXiv · 1512.06884

The blow-up rate for strongly perturbed semilinear wave equations in the conformal regime without a radial assumption

Mohamed-Ali Hamza

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Abstract

We consider in this paper a large class of perturbed semilinear wave equations with critical (in the conformal transform sense) power nonlinearity. We will show that the blow-up rate of any singular solution is given by the solution of the non-perturbed associated ODE. The result in the radial case has been proved in [13]. The same approach will be followed here, but the main difference is to construct a Lyapunov functional in similarity variables valid in the non-radial case, which is far from being trivial. That functional is obtained by combining some classical estimates and a new identity of the Pohozaev type.

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Mohamed-Ali Hamza. 2015-12-21. The blow-up rate for strongly perturbed semilinear wave equations in the conformal regime without a radial assumption. https://arxiv.org/abs/1512.06884

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