The Cauchy problem for Kirchhoff equations
Tóm tắt
Từ khóa
Tài liệu tham khảo
[A] A. Arosio,Averaged evolution equations…, to appear on 2nd. Workshop on functional analytic Methods in Complex Analysis (Proc. Trieste 1993), World Scientific.
[AS] A. Arosio & S. Spagnolo,Global solutions to the Cauchy problem for a nonlinear hyperbolic equation, in Nonlinear P.D.E. Collège de France Seminars. VI, Brézis-Lions eds., Pitman Notes Math. 109 (1984), 1–26.
[B] S. Bernstein,Sur une classe d'équations fonctionnelles aux dérivées partielles, Izv. Akad. Nauk. SSSR, Ser. Mat. 4 (1940), 17–20.
[CDS] F. Colombini, E. De Giorgi & S. Spagnolo,Sur les équations hyperboliques avec des coefficients… Ann. S.N.S. Pisa 6 (1979), 511–559.
[CS] F. Colombini & S. Spagnolo,An example of weakly hyperbolic Cauchy problem not well posed in C ∞ Acta Math. 148 (1982), 243–253.
[DS1] P. D'Ancona & S. Spagnolo,Global solvability for the degenerate Kirchhoff equation…, Inv. Mat. 108 (1992), 247–262.
[DS2] P. D'Ancona & S. Spagnolo,On an abstract weakly hyperbolic equation modelling…, in Developments in P. D. E. and Appl. to Math. Phys., ed. by G. Buttazzo, G.P. Galdi & L. Zanghirati, Plenum (London) 1993, 27–32.
[DS3] P. D'Ancona & S. Spagnolo,A class of nonlinear hyperbolic problems with global solutions, to appear in Arch. Rat. Mech. Anal. (pre-print Dip. Mat. Pisa 631, 1991).
[K] G. Kirchhoff,Vorlesungen uber Mechanick, Teubner, Leipzig, 1883.
[KY] K. Kajitani & K. Yamaguti,On global real analytic solutions of the degenerate Kirchhoff equation, Inst. Math. Univ. of Tsukuba, (1993).
[MM] L.A. Medeiros & M. Miranda,Solutions for the equations of non-linear vibrations in Sobolev spaces of fractionary order, Comp. Appl. Math 6 (1987), 257–267.