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Asymptotic behavior of solutions to perturbed superstable wave equations. / Kmit, I. Y.; Lyulko, N. A.

In: Journal of Physics: Conference Series, Vol. 894, No. 1, 012056, 22.10.2017.

Research output: Contribution to journal › Article › peer-review

Harvard

Kmit, IY & Lyulko, NA 2017, 'Asymptotic behavior of solutions to perturbed superstable wave equations', Journal of Physics: Conference Series, vol. 894, no. 1, 012056. https://doi.org/10.1088/1742-6596/894/1/012056

APA

Kmit, I. Y., & Lyulko, N. A. (2017). Asymptotic behavior of solutions to perturbed superstable wave equations. Journal of Physics: Conference Series, 894(1), [012056]. https://doi.org/10.1088/1742-6596/894/1/012056

Vancouver

Kmit IY, Lyulko NA. Asymptotic behavior of solutions to perturbed superstable wave equations. Journal of Physics: Conference Series. 2017 Oct 22;894(1):012056. doi: 10.1088/1742-6596/894/1/012056

Author

Kmit, I. Y. ; Lyulko, N. A. / Asymptotic behavior of solutions to perturbed superstable wave equations. In: Journal of Physics: Conference Series. 2017 ; Vol. 894, No. 1.

BibTeX

@article{ea3d303ee9a44fbdba9eeeee59130146,
title = "Asymptotic behavior of solutions to perturbed superstable wave equations",
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 × L 2-initial data.",
keywords = "1ST-ORDER HYPERBOLIC SYSTEMS, INITIAL-BOUNDARY PROBLEMS, STABILIZATION",
author = "Kmit, {I. Y.} and Lyulko, {N. A.}",
year = "2017",
month = oct,
day = "22",
doi = "10.1088/1742-6596/894/1/012056",
language = "English",
volume = "894",
journal = "Journal of Physics: Conference Series",
issn = "1742-6588",
publisher = "IOP Publishing Ltd.",
number = "1",

}

RIS

TY - JOUR

T1 - Asymptotic behavior of solutions to perturbed superstable wave equations

AU - Kmit, I. Y.

AU - Lyulko, N. A.

PY - 2017/10/22

Y1 - 2017/10/22

N2 - 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 × L 2-initial data.

AB - 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 × L 2-initial data.

KW - 1ST-ORDER HYPERBOLIC SYSTEMS

KW - INITIAL-BOUNDARY PROBLEMS

KW - STABILIZATION

UR - http://www.scopus.com/inward/record.url?scp=85033239320&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/894/1/012056

DO - 10.1088/1742-6596/894/1/012056

M3 - Article

AN - SCOPUS:85033239320

VL - 894

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012056

ER -

ID: 9699773