The paper deals with initial-boundary value problems for linear nonautonomous first order hyperbolic systems whose solutions stabilize to zero in a finite time for any initial data. We prove that for any small bounded perturbations the perturbed problems are asymptotically exponentially stable. We describe a class of boundary conditions for which the solutions to the perturbed problems become eventually smooth.
Finite Time Stabilization of Nonautonomous First Order Hyperbolic Systems
Convective stability in scalar balance laws
Nonlinear stability of periodic roll solutions in the real Ginzburg-Landau equation against $C_{\mathrm{ub}}^m$-perturbations
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