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Strong asymptotic stability for a beam equation with weak damping

Published online by Cambridge University Press:  14 November 2011

Eduard Feireisl
Eduard Feireisl
Affiliation:
Institute of Mathematics of the Czechoslovak Academy of Sciences. Žitná 25, 115 67 Praha 1, Czechoslovakia
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Synopsis

Any solution to the problem

is shown to decay to zero in the strong topology of the energy space as t→ ∞. The function β is allowed to be nonmonotone and d is a nonnegative function strictly positive on a nonvoid subset of (0, л).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 365 - 371
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Bahri, A., These de 3-ème cycle (Université de Paris VI, June 1979).Google Scholar
2Chang, K. C. and Sanchez, L.. Nontrivial periodic solutions of a nonlinear beam equation. Math. Methods Appl. Sci. 4 (1982) 194–205.CrossRefGoogle Scholar
3Dafermos, C. M.. Asymptotic behavior of solutions of evolution equations. In Nonlinear Evolution Equations, ed. Crandall, M. G., 103–123 (New York: Academic Press, 1978).Google Scholar
4Feireisl, E.. Strong decay for wave equations with nonlinear nonmonotone damping. Nonlinear Anal, (to appear).Google Scholar
5Haraux, A.. Nonlinear evolution equations—Global behavior of solutions, Lecture Notes in Mathematics 841 (Berlin: Springer, 1980).Google Scholar
6Haraux, A.. Stabilization of trajectories for some weakly damped hyperbolic equations. J. Differential Equations 59 (1985) 145–154.CrossRefGoogle Scholar
7Lions, J. L. and Magenes, E.. Problemes awe limites nonhomogenes et applications I (Paris: Dunod, 1968).Google Scholar
8Rudin, W.. Functional Analysis (New York: McGraw-Hill, 1973).Google Scholar
9Slemrod, M.. Weak asymptotic decay via a “relaxed invariance principle” for a wave equation with nonlinear, nonmonotone damping. Proc.Roy. Soc. Edinburgh Sect. A 113 (1989) 87–97.CrossRefGoogle Scholar