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Convergence to steady states of solutions of semilinear evolutionary integral equations

Authors:	Ralph Chill Eva Fa?angová

Institution:	(1) Abteilung Angewandte Analysis, Universität Ulm, 89069 Ulm, Germany;(2) Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Abstract:	We study the convergence and decay rate to a steady state of bounded solutions of the nonlinear evolutionary integral equation $\ddot{u} + B_0 \dot{u} + a(B_1 \dot{u}) + {\mathcal M} (u) = 0 ,$ and we apply our abstract results to the viscoelastic Euler-Bernoulli beam and to Kelvin-Voigt solids.Received: 25 March 2003, Accepted: 5 April 2004, Published online: 16 July 2004This work was partially supported by the DFG project Regularität und Asymptotik für elliptische und parabolische Probleme* and by the grants GAR 201/01/D094, MSM 113200007.

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