Perturbations of superstable linear hyperbolic systems

2016/05/16 by Kmit, I., Lyul'ko, N.
#35B20 #35B35 #35B40 #35B45 #35B65 #35L50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.04703

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.

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