Document Type

Article

Publication Date

2016

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.

Comments

Posted with permission. Version of record appears here:

M. Beceanu and A. Soffer, "A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions," arXiv:1605.07713v2 [math.AP] Jun. 2016.

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