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A hyperbolic problem of second order with unilateral constraints: The vibrating string with a concave obstacle. (English) Zbl 0497.73059


MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K05 Strings
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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[1] Amerio, L., Su un problema di vicoli unilaterali per l’equazione non omogenea della corda vibrante, IAC (Ist. Appl.Calc. “Mauro Picone”) Publ., Ser. D, 109, 3-11 (1976) · Zbl 0432.73062
[2] Amerio, L., On the motion of a string vibrating through a moving ring with a continuously variable diameter, Att. Acad. Naz. Lincei Rend., 62, 134-142 (1977) · Zbl 0378.73057
[3] Amerio, L.; Prouse, G., Study of the motion of a string vibrating against an obstacle, Rend. Mat., 2, 563-585 (1975) · Zbl 0327.73070
[4] A. Bamberger and M. Schatzman; A. Bamberger and M. Schatzman
[5] Brezis, H., Opérateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert (1973), North-Holland and American Elsevier: North-Holland and American Elsevier Amsterdam/London/New York · Zbl 0252.47055
[6] Citrini, C., Sull’urto parzialmente elastico o anelastico di una corda vibrante contro un ostacolo, Atti Accad. Naz. Lincei Rend., 59, 5, 368-376 (1975) · Zbl 0351.70018
[7] Citrini, C., Sull’urto parzialmente elastico o anelastico di una corda vibrante contro un ostacolo, Atti Accad. Naz. Lincei Rend., 59, 6, 667-676 (1975) · Zbl 0355.73065
[8] Citrini, C., The energy theorem in the impact of a string vibrating against a point shaped obstacle, Atti Accad. Naz. Lincei Rend., 62, 143-149 (1977) · Zbl 0384.70035
[9] Courant, R.; Hilbert, D., Methods of Mathematical Physics (1962), Interscience: Interscience New York/London · Zbl 0729.00007
[10] Hewitt, E.; Stromberg, K., Real and Abstract Analysis (1965), Springer-Verlag: Springer-Verlag New York/Heidelberg/Berlin
[11] L. Landau and E. Lifschitz; L. Landau and E. Lifschitz · Zbl 0146.23803
[12] M. Schatzman; M. Schatzman · Zbl 0405.35047
[13] Schwartz, L., Théorie des distributions (1966), Hermann: Hermann Paris
[14] Amerio, L.; Prouse, G., (A lecture in the Collège de France was delivered on the subject by L. Amerio (June, 1978)), paper to appear
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