On extended lifespan for 1d damped wave equation
Kazumasa Fujiwara, Vladimir Georgiev
TL;DR
This paper investigates the lifespan of solutions to the one-dimensional semilinear damped wave equation, providing sharp estimates and demonstrating extended lifespan under specific initial conditions, along with the existence of some global solutions.
Contribution
It offers a new sharp lifespan estimate for the 1D damped wave equation when initial position and speed sum to zero, extending previous results.
Findings
Extended lifespan under specific initial conditions
Existence of some global solutions
Sharp lifespan estimates derived
Abstract
In this manuscript, a sharp lifespan estimate of solutions to semilinear classical damped wave equation is investigated in one dimensional case, when the sum of initial position and speed is pointwisely. Especially, an extension of lifespan is shown in this case. Moreover, existence of some global solutions are obtained by a direct computation.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations