Abstract
This letter investigates the boundary feedback control for a class of semi-linear hyperbolic partial differential equations with nonlinear relaxation, which is local Lipschitz continuous with a stable matrix structure. A sufficient condition in terms of linear inequalities is developed for the existence of global Cauchy solutions and the exponential stability by seeking a balance between the relaxation term and the boundary condition. These results are illustrated with an application to the boundary feedback control for a class of hyperbolic Lotka–Volterra models.
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