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Perturbations of superstable linear hyperbolic systems. / Kmit, Irina; Lyul'ko, Natalya.

In: Journal of Mathematical Analysis and Applications, Vol. 460, No. 2, 15.04.2018, p. 838-862.

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

Harvard

Kmit, I & Lyul'ko, N 2018, 'Perturbations of superstable linear hyperbolic systems', Journal of Mathematical Analysis and Applications, vol. 460, no. 2, pp. 838-862. https://doi.org/10.1016/j.jmaa.2017.12.030

APA

Kmit, I., & Lyul'ko, N. (2018). Perturbations of superstable linear hyperbolic systems. Journal of Mathematical Analysis and Applications, 460(2), 838-862. https://doi.org/10.1016/j.jmaa.2017.12.030

Vancouver

Kmit I, Lyul'ko N. Perturbations of superstable linear hyperbolic systems. Journal of Mathematical Analysis and Applications. 2018 Apr 15;460(2):838-862. doi: 10.1016/j.jmaa.2017.12.030

Author

Kmit, Irina ; Lyul'ko, Natalya. / Perturbations of superstable linear hyperbolic systems. In: Journal of Mathematical Analysis and Applications. 2018 ; Vol. 460, No. 2. pp. 838-862.

BibTeX

@article{656b7adeabdf4a8fb8b1d9fa07ef42aa,
title = "Perturbations of superstable linear hyperbolic systems",
abstract = "The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in L2 as well as in C1 under small bounded perturbations. To show this for C1, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually C1-smooth for any L2-initial data.",
keywords = "Bounded perturbations, Evolution family, Exponential stability, First order hyperbolic systems, Smoothing boundary conditions, Superstability, SEMIGROUPS, SUPER-STABILITY, INITIAL-BOUNDARY PROBLEMS, STABILIZATION, WAVE-EQUATION, NETWORKS",
author = "Irina Kmit and Natalya Lyul'ko",
year = "2018",
month = apr,
day = "15",
doi = "10.1016/j.jmaa.2017.12.030",
language = "English",
volume = "460",
pages = "838--862",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Perturbations of superstable linear hyperbolic systems

AU - Kmit, Irina

AU - Lyul'ko, Natalya

PY - 2018/4/15

Y1 - 2018/4/15

N2 - The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in L2 as well as in C1 under small bounded perturbations. To show this for C1, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually C1-smooth for any L2-initial data.

AB - The paper deals with initial-boundary value problems for linear non-autonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in L2 as well as in C1 under small bounded perturbations. To show this for C1, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually C1-smooth for any L2-initial data.

KW - Bounded perturbations

KW - Evolution family

KW - Exponential stability

KW - First order hyperbolic systems

KW - Smoothing boundary conditions

KW - Superstability

KW - SEMIGROUPS

KW - SUPER-STABILITY

KW - INITIAL-BOUNDARY PROBLEMS

KW - STABILIZATION

KW - WAVE-EQUATION

KW - NETWORKS

UR - http://www.scopus.com/inward/record.url?scp=85038350285&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2017.12.030

DO - 10.1016/j.jmaa.2017.12.030

M3 - Article

AN - SCOPUS:85038350285

VL - 460

SP - 838

EP - 862

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -

ID: 10065855