arXiv subjects

N. Lyul'ko

Publications and source records attributed to N. Lyul'ko.

2 recordsLinked to original sources

arXiv2018

Perturbations of superstable linear hyperbolic systems

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 $L^2$ as well as in $C^1$ under small bounded perturbations. To show this for $C^1$, we prove a general smoothing result implying that the solutions to the perturbed problems become eventually $C^1$-smooth for any $L^2$-initial data.

math.AP↗

arXiv2018

Exponential stability of solutions to perturbed superstable wave equations

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 $H^1\times L^2$-initial data.

math.AP↗