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arXiv · 1801.02856

Exponential stability of solutions to perturbed superstable wave equations

I. Kmit·N. Lyul'ko
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Abstract

The paper deals with initial-boundary value problems for the linear wave equation whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^2$ under small bounded perturbations of the wave operator. To show this for $C^2$, we prove a smoothing result implying that the solutions to the perturbed problems become eventually $C^2$-smooth for any $H^1\times L^2$-initial data.

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I. Kmit, N. Lyul'ko. 2018-01-09. Exponential stability of solutions to perturbed superstable wave equations. https://doi.org/10.48550/arxiv.1801.02856

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