Blow up and lifespan estimates for systems of semi-linear wave equations with damping and potential
Mengliang Liu
TL;DR
This paper investigates blow-up phenomena and lifespan estimates for semi-linear wave systems with damping and potential, showing they behave similarly to systems without these effects.
Contribution
It extends existing blow-up and lifespan results to systems with space-dependent damping and potential, a case not thoroughly analyzed before.
Findings
Blow-up regions are identical to those without damping and potential.
Lifespan estimates match the undamped, potential-free systems.
Results apply to three types of wave systems.
Abstract
In this paper, we consider the semi-linear wave systems with power-nonlinearities and a large class of space-dependent damping and potential. We obtain the same blow-up regions and the lifespan estimates for three types wave systems, compared with the systems without damping and potential.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering