Bounds for contractive semigroups and second order systems

2004/04/06 by Kresimir Veselic, Veselic, Kresimir
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #math.DS #math.FA

paper · pdf · doi:10.48550/arxiv.math/0404120

arxiv created 2004/04/06 · arxiv updated 2009/12/01

Abstract

We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order systems with fairly general operator coefficients and apply our bound to the perturbation of the damping term. The result is illustrated on a dissipative wave equation. As a consequence the exponential decay of some second order systems is proved.

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