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In this paper we consider the initial-boundary value problem for the nonlinear wave equation.
Wydawca
Czasopismo
Rocznik
Tom
Strony
365--392
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
autor
- Department of Mathematics and Computer Science University of Natural Science Vietnam National University Hochiminh City 227 Nguyen Van Cu Str. Dist. 5, Hochiminh City, Vietnam, lingnt@hcmc.netnam.vn
Bibliografia
- [1] R. A. Adams, Sobolev Spaces, Academic Press, NewYork, 1975.
- [2] D.T.T. Binh, A. P. N. Dinh, N.T. Long, Linear recursive schemes associated with the nonlinear wave equation involving Bessel's operator, Math. Comp. Modelling, 34 (2001), 541-556.
- [3] G.F. Carrier, On the nonlinear vibrations problem of elastic string, Quart. J. Appl. Math. 3 (1945), 157-165.
- [4] A. P. N. Dinh, N. T. Long, Linear approximation and asymptotic expansion associated to the nonlinear wave equation in one dimension, Demonstratio Math. 19 (1986), 45-63.
- [5] Y. Ebihara, L. A. Medeiros, M. M. Miranda, Local solutions for a nonlinear degenerate hyperbolic equation, Nonlinear Anal. 10 (1986), 27-40.
- [6] M. Hosoya, Y. Yamada, On some nonlinear wave equation I: Local existence and regularity of solutions, J. Fac. Sci. Univ. Tokyo. Sect. IA, Math. 38 (1991), 225-238.
- [7] G. R. Kirchhoff, Vorlesungen über Mathematische Physik: Mechanik, Teuber, Leipzig, 1876, Section 29.7.
- [8] N. T. Long, et al., On the nonlinear vibrations equation with a coefficient containing an integral, Comput. Math. Math. Phys. 33 (1993), 1171-1178.
- [9] N. T. Long, T. N. Diem, On the nonlinear wave equation utt-uxx = f(x, t, u, ux, ut) associated with the mixed homogeneous conditions, Nonlinear Anal. 29 (1997), 1217-1230.
- [10] N. T. Long, A. P. N. Dinh, D. T. T. Binh, Mixed problem for some semilinear wave equation involving Bessel's operator, Demonstratio Math. 32 (1999), 77-94.
- [11] N. T.Long, A. P. N. Dinh, T. N. Diem, Linear recursive schemes and asymptotic expansion associated with the Kirchhoff-Carrier operator, J. Math. Anal. Appl. 267 (2002), 116-134.
- [12] N. T. Long, On the nonlinear wave equation utt -B(t, //ux//2)uxx = f(x, t, u, ux, ut) associated with the mixed homogeneous conditions, J. Math. Anal. Appl. 274 (2002),102-123.
- [13] N. T. Long, Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions, Electron. J. Differential Equations, Vol. 2005 (2005), No. 138, 1-18.
- [14] L. A. Medeiros, On some nonlinear perturbation of Kirchhoff-Carrier operator, Comp. Appl. Math. 13 (1994), 225-233.
- [15] L.A. Medeiros, J. Limaco, S. B. Menezes, Vibrations of elastic strings: Mathematical aspects, Partone, J. Comput. Anal. Appl. 4, No. 2 (2002), 91-127.
- [16] L.A. Medeiros, J. Limaco, S. B. Menezes, Vibrations of elastic strings: Mathematical aspects, Part two, J. Comput. Anal. Appl. 4, No. 3 (2002), 211-263.
- [17] S. I. Pohozaev, On a class of quasilinear hyperbolic equation, Math. USSR. Sb. 25 (1975), 145-158.
- [18] E. L. Orti z, A. P. N. Dinh, Linear recursive schemes associated with some nonlinear partial differential equations in one dimension and the Tau method, SIAM J. Math.Anal. 18 (1987), 452-464.
- [19] R. E. Showalter, Hilbert space methods for partial differential equations, Electronic J. Diff. Equat., Monograph 01, 1994.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0034-0009