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 -