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Bounds for contractive semigroups and second order systems

Kresimir Veselic
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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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Kresimir Veselic. 2004-04-06. Bounds for contractive semigroups and second order systems. https://arxiv.org/abs/math/0404120

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