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arXiv · 1605.07713

A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions

Marius Beceanu·Avy Soffer
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Abstract

In dimensions one to three, the fundamental solution to the free wave equation is positive. Therefore, there exists a simple positivity criterion for solutions. We use this to obtain large global solutions to two well-studied energy-supercritical semilinear wave equations, as well as some new results in the subcritical and critical cases.

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Marius Beceanu, Avy Soffer. 2016-05-25. A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions. https://arxiv.org/abs/1605.07713

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