The lifespan of solutions to semilinear wave equations with scale invariant damping in one space dimension (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

This note is a summary of the result in Wakasa [10]. We consider the semilinear wave equations with special scale invariant damping in one space dimension. The equation can be reduced to some nonlinear wave equations under some transformation. Making use of the iteration argument of John [5], we get the sharp estimates of the lifespan. Also, we show that if the initial data are odd functions, then the critical exponent changes. This fact follows from the special property of the solution of the wave equation in one space dimension.