A new class of small initial data which may shift the critical power and lifespan estimates for the classical damped wave equations

Abstract

In this manuscript, lifespan of solutions to semilinear classical damped wave equations is investigated when the sum of initial position and speed is $ 0 $ pointwisely. The results in the existing literature are considered mainly in the case when the sum is positive. Here, it is shown that lifespan is extended with appropriate initial data with modified ODE approach. The result implies that the blowup mechanics for semilinear damped wave equations cannot be directly described by using the scaling property and the corresponding weak form approach. The results in this work leave different directions for further study of the lifespan behavior of the solutions to semilinear damped wave equations.