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On a uniqueness theorem of L. Amerio and G. Prouse

Published online by Cambridge University Press:  14 November 2011

Alain Haraux
Alain Haraux
Affiliation:
Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique (LA 189), Tour 55–65 – 5 éme étage, 4, place Jussieu, 75230 Paris Cédex 05, France
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Synopsis

We give two generalizations of a theorem of L. Amerio and G. Prouse concerning uniqueness of the almost-periodic solution of the wave equation with a local multivalued damping term and almost-periodic forcing.

Counterexamples are given which show that these results may fail if some hypotheses of the theorems are dropped. They also show that the two generalizations are relatively independent.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 221 - 230
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Amerio, L. and Prouse, G.. Uniqueness and almost-periodicity theorems for a nonlinear wave equation. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 46 (1969), 1–8.Google Scholar
2Biroli, M.. Bounded or almost-periodic solutions of the nonlinear vibrating membrane equation. Ricerche Mat. 22 (1973), 190–202.Google Scholar
3Biroli, M. and Haraux, A.. Asymptotic behavior for an almost periodic, strongly dissipative wave equation. J. Differential Equations 38 (1980), 422–440.CrossRefGoogle Scholar
4Brezis, H.. Opérateurs maximaux monotones et semi-groups de contractions dans les espaces de Hilbert (Amsterdam: North-Holland, 1973).Google Scholar
5Brezis, H.. Problemes unilatéraux. J. Math. Pures Appl. 51 (1972), 1–168.Google Scholar
6Brezis, H.. Integrates convexes dans les espaces de Sobolev. Israel J. Math. 13 (1972), 9–23.CrossRefGoogle Scholar
7Grun-Rehomme, M.. Caractérisation du sous-difterentiel d'integrandes convexes dans les espaces de Sobolev. J. Math. Pures Appl. 56 (2) (1977), 149–156.Google Scholar
8Haraux, A.. Thése, University of Paris VI (1978) (ch. E).Google Scholar
9Haraux, A.. Comportement à l'infini pour certains systémes dissipatifs non linéaires. Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), 213–234.CrossRefGoogle Scholar
10Haraux, A.. Forced oscillations for some nonlinear, weakly dissipative wave equations. J. Differential Equations 44 (1982), 440–451.CrossRefGoogle Scholar
11Haraux, A.. Almost-periodic forcing for a wave equation with a nonlinear, local damping term. Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 195–212.CrossRefGoogle Scholar