A Positivity Criterion for the Wave Equation and Global Existence of   Large Solutions
  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. 
Marius Beceanu, Avy Soffer
math.AP