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

Authors

Marius Beceanu, University at Albany, State University of New YorkFollow
Avy Soffer, Rutgers University - New Brunswick/Piscataway

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.

Recommended Citation

Beceanu, Marius and Soffer, Avy, "A Positivity Criterion for the Wave Equation and Global Existence of Large Solutions" (2016). Mathematics and Statistics Faculty Scholarship. 11.
https://scholarsarchive.library.albany.edu/math_fac_scholar/11