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arXiv · 1804.03978

A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimension

Alessandro Palmieri
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Abstract

In the present article a semilinear wave equation with scale-invariant damping and mass is considered. The global (in time) existence of radial symmetric solutions in even spatial dimension $n$ is proved using weighted $L^\infty-L^\infty$ estimates, under the assumption that the multiplicative constants, which appear in the coefficients of damping and of mass terms, fulfill an interplay condition which yields somehow a "wave-like" model. In particular, combining this existence result with a recently proved blow-up result, a suitable shift of Strauss exponent is proved to be the critical exponent for the considered model. Moreover, the still open part of a conjecture done by D'Abbicco - Lucente - Reissig is proved to be true in the massless case.

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Alessandro Palmieri. 2018-04-11. A global existence result for a semilinear wave equation with scale-invariant damping and mass in even space dimension. https://doi.org/10.1002/mma.5542

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