Uniform stabilization of an acoustic system
Ka\"is Ammari, Fathi Hassine, Luc Robbiano
TL;DR
This paper investigates how to achieve exponential decay of solutions in an acoustic system through spatially distributed damping, under certain structural assumptions on the damping term.
Contribution
It provides conditions under which the acoustic system's solutions exponentially decay, advancing understanding of stabilization with distributed damping.
Findings
Exponential decay of solutions is achieved under specific damping conditions.
Structural properties of damping are crucial for stabilization.
The results apply to acoustic systems with spatially distributed damping.
Abstract
We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we identify exponential decay of solutions with growing time.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering · Advanced Mathematical Physics Problems