Perturbations of superstable linear hyperbolic systems

Perturbations of superstable linear hyperbolic systems Full article

Journal

Journal of Mathematical Analysis and Applications
ISSN: 0022-247X , E-ISSN: 1096-0813

Output data

Year: 2018, Volume: 460, Number: 2, Pages: 838-862 Pages count : 25 DOI: 10.1016/j.jmaa.2017.12.030

Tags

Bounded perturbations; Evolution family; Exponential stability; First order hyperbolic systems; Smoothing boundary conditions; Superstability

Authors

Kmit I. ^1,2 , Lyul`ko N.A. ^3,4

Affiliations

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

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 L2as well as in C1under 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.

Kmit I. , Lyul`ko N.A.
Perturbations of superstable linear hyperbolic systems
Journal of Mathematical Analysis and Applications. 2018. V.460. N2. P.838-862. DOI: 10.1016/j.jmaa.2017.12.030 WOS Scopus OpenAlex

Web of science:	WOS:000425705800021
Scopus:	2-s2.0-85038350285
OpenAlex:	W2964209204

DB	Citing
Scopus	10
OpenAlex	13
Web of science	6