Fourth order quasilinear evolution equations of hyperbolic type

Alberto AROSIO; Roberto NATALINI; Maria Gabriella PAOLI

doi:10.2969/jmsj/04440619

Alberto AROSIO, Roberto NATALINI, Maria Gabriella PAOLI

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 4 Pages 619-630

DOI https://doi.org/10.2969/jmsj/04440619

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Published: 1992 Received: December 26, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Dipartimento di Matematice

Right :
1) Dipartimento di Matematica

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : A) A. Arosio, On the nonlinear Timoshenko-Kirchhoff beam equation, Quad. Dip. Mat. Univ. Parma, 61 (1990).
AG) A. Arosio and S. Garavaldi, On the mildly degenerate Kirchhoff string, Math. Methods Appl. Sci., 14 (1991), 177-195.
ANPP) A. Arosio, R. Natalini, S. Panizzi and M. G. Paoli, Fourth order abstract evolution equations, to appear in Nonlinear hyperbolic equations, Proc. Varenna 1990, (eds. M.K.V. Murthy and S. Spagnolo), Res. Notes Mather., Longman, Harlow.
AP) A. Arosio and S. Panizzi, Global bounded weak solutions for an abstract nonlinear Timoshenko beam equation with four propagation speeds, Funkcial. Ekvac., to appear.
APP1) A. Arosio, S. Panizzi and M. G. Paoli, Inhomogeneous Timoshenko beam equations, short communication at 5th Symposium on control of distributed parameter system (Perpignan, June 1989), Math. Mech. Appl. Sci., to appear.
APP2) A. Arosio, S. Panizzi and M. G. Paoli, Temporally inhomogeneous Timoshenko beam equations, Ann. Mat. Pura Appl., to appear.
HR) M. H. Sapir and E. L. Reiss, Dynamic buckling of a nonlinear Timoshenko beam, SIAM J. Appl. Math., 37 (1979), 290-301.
K) T. Kato, Abstract Differential Equations and Nonlinear Mixed Problems, Lezioni Fermiane, Scuola Normale Superiore, Pisa, 1985.
Ka) H. Kauderer, Nichtlineare mechanik, Part 2, B II, §1.88 b, Springer, Berlin, 1958.
Ki) G. Kirchhoff, Mechanik, ch. 29 §7, 3rd ed., Teubner, Leipzig, 1883.
N) R. Narasimha, Nonlinear vibration of an elastic string, J. Sound Vibration, 8 (1968), 134-146.
NM) A. H. Nayfeh and D. T. Mook, Nonlinear oscillations, ch. 7, Wiley-Interscience, New York, 1979.
P) S. Panizzi, Abstract nonlinear Timoshenko beam equation, Rend. Sem. Mat. Univ. Padova, to appear.
T) S.P. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine, 41 (1921), 744-746. (reprinted in Collected papers, McGraw-Hill, New York, 1953, cf, also Vibration problems in engineering, 3rd ed., Van Nostrand, Princeton, 1955).
Tu) M. Tucsnak, On the Initial and Boundary Value Problem for the Nonlinear Timoshenko Beam, An. Acad, bras. Ci., 63(2) (1991), 115-125.

Right : [A] A. Arosio, On the nonlinear Timoshenko-Kirchhoff beam equation, Quad. Dip. Mat. Univ. Parma, 61 (1990).
[AG] A. Arosio and S. Garavaldi, On the mildly degenerate Kirchhoff string, Math. Methods Appl. Sci., 14 (1991), 177-195.
[ANPP] A. Arosio, R. Natalini, S. Panizzi and M. G. Paoli, Fourth order abstract evolution equations, to appear in Nonlinear hyperbolic equations, Proc. Varenna 1990, (eds. M. K. V. Murthy and S. Spagnolo), Res. Notes Mather., Longman, Harlow.
[AP] A. Arosio and S. Panizzi, Global bounded weak solutions for an abstract nonlinear Timoshenko beam equation with four propagation speeds, Funkcial. Ekvac., to appear.
[APP1] A. Arosio, S. Panizzi and M. G. Paoli, Inhomogeneous Timoshenko beam equations, short communication at 5th Symposium on control of distributed parameter system (Perpignan, June 1989), Math. Mech. Appl. Sci., to appear.
[APP2] A. Arosio, S. Panizzi and M. G. Paoli, Temporally inhomogeneous Timoshenko beam equations, Ann. Mat. Pura Appl., to appear.
[HR] M. H. Sapir and E. L. Reiss, Dynamic buckling of a nonlinear Timoshenko beam, SIAM J. Appl. Math., 37 (1979), 290-301.
[K] T. Kato, Abstract Differential Equations and Nonlinear Mixed Problems, Lezioni Fermiane, Scuola Normale Superiore, Pisa, 1985.
[Ka] H. Kauderer, Nichtlineare mechanik, Part 2, B II, §1.88 b, Springer, Berlin, 1958.
[Ki] G. Kirchhoff, Mechanik, ch. 29 §7, 3rd ed., Teubner, Leipzig, 1883.
[N] R. Narasimha, Nonlinear vibration of an elastic string, J. Sound Vibration, 8 (1968), 134-146.
[NM] A. H. Nayfeh and D. T. Mook, Nonlinear oscillations, ch. 7, Wiley-Interscience, New York, 1979.
[P] S. Panizzi, Abstract nonlinear Timoshenko beam equation, Rend. Sem. Mat. Univ. Padova, to appear.
[T] S. P. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine, 41 (1921), 744-746. (reprinted in Collected papers, McGraw-Hill, New York, 1953, cf, also Vibration problems in engineering, 3rd ed., Van Nostrand, Princeton, 1955).
[Tu] M. Tucsnak, On the Initial and Boundary Value Problem for the Nonlinear Timoshenko Beam, An. Acad, bras. Ci., 63 (2) (1991), 115-125.

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