Asymptotic behavior of solutions to perturbed superstable wave equations

Asymptotic behavior of solutions to perturbed superstable wave equations Full article

Journal

Journal of Physics: Conference Series
ISSN: 1742-6588 , E-ISSN: 1742-6596

Output data

Year: 2017, Volume: 894, Article number : 012056, Pages count : 7 DOI: 10.1088/1742-6596/894/1/012056

Authors

Kmit I.Y. ^1,2 , Lyulko N.A. ^3,4

Affiliations

1	Humboldt University of Berlin
2	Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine
3	Sobolev Institute of Mathematics of Russian Academy of Sciences
4	Novosibirsk State University, Novosibirsk, Russia

The paper deals with initial-boundary value problems for the linear wave equation whose solutions stabilize to zero in a nite time. We prove that problems in this class remain exponentially stable in L2 as well as in C2 under small bounded perturbations of the wave operator. To show this for C2, we prove a smoothing result implying that the solutions to the perturbed problems become eventually C2-smooth for any H1 L2-initial data.

Kmit I.Y. , Lyulko N.A.
Asymptotic behavior of solutions to perturbed superstable wave equations
Journal of Physics: Conference Series. 2017. V.894. 012056 :1-7. DOI: 10.1088/1742-6596/894/1/012056 Scopus OpenAlex

Scopus:	2-s2.0-85033239320
OpenAlex:	W2766425486

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