Exponential Decay of Solution Energy for Equations Associated with Some Operator Models of Mechanics |
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Authors: | R O Hryniv A A Shkalikov |
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Institution: | (1) Institute for Applied Problems of Mechanics and Mathematics, Lviv, Ukraine;(2) Department of Mechanics and Mathematics, Moscow State University, Russia |
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Abstract: | We consider the equation
in a Hilbert space , where A is a uniformly positive self-adjoint operator and B is a dissipative operator. The main result is the proof of a theorem stating the exponential energy decay for solutions of this equation (or the exponential stability of the semigroup associated with the equation) under the additional assumption that B is sectorial and is subordinate to A in the sense of quadratic forms. |
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Keywords: | stability of motion stability of semigroups operator equations operator models in mechanics |
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