An estimate of the interval of existence of solutions of the nonlinear Kirchhoff equation

Computers and Mathematics with Applications

Volumn 31, Issue 2, 1996, Pages 63-65

  Bainov, D ^a   Minchev, E ^a  

^a MEDICAL UNIVERSITY OF SOFIA   (Bulgaria)

Author keywords

An estimate; Interval of existence of solutions; Nonlinear Kirchhoff equation

Indexed keywords

EID: 0042038969     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/0898-1221(95)00193-X     Document Type: Article

References (11)

1. G. Kirchhoff, Vorlesungen über Mechanik, Teubner, Leipzig, (1883).
2. P. D'Ancona and S. Spagnolo, Global existence for the generalized Kirchhoff equation with small data, Arch. Rat. Mech. Anal. (to appear).
3. P. D'Ancona and S. Spagnolo, Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108, 247-262 (1992).
4. P. D'Ancona and S. Spagnolo, Nonlinear perturbations of the Kirchhoff equation, Comm. Pure Appl. Math. XLVII (7), 1005-1029 (1994).
5. R.W. Dickey, Infinite systems of nonlinear oscillation equations, J. Diff. Equations 8, 16-26 (1970).
6. R.W. Dickey, Infinite systems of nonlinear oscillation equations related to the string, Proc. Amer. Math. Soc. 23, 459-468 (1969).
7. R.W. Dickey, Infinite systems of nonlinear oscillation equations with linear damping, SIAM J. Appl. Math. 19, 208-214 (1970).
8. L.A. Medeiros, On a new class of nonlinear wave equations, J. Math. Anal. Appl. 69, 252-262 (1979).
9. L.A. Medeiros and M. Miranda, Solutions for the equations of nonlinear vibrations in Sobolev spaces of fractionary order, Comp. Appl. Math. 6, 257-267 (1987).
10. S. Spagnolo, The Cauchy problem for Kirchhoff equations, Rendiconti del Seminario Matematico e Fisico Di Milano LXII, 17-51 (1992).
11. 1+α, J. Fac. Sci. Univ. Tokyo, Sect. IA 13, 109-124 (1966).