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On the nonlinear wave equation with the mixed nonhomogenous conditions: linear approximation and asymptotic expansion of solutions

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Języki publikacji
EN
Abstrakty
EN
In this paper we consider the following nonlinear wave equation (1) utt-uxx = f(x,t,u,ux,ut), x is an element of (0,l), 0 < t < T, (2) ux(0,t)-hou(0,t)=go(t), u(1,t) = g1(t), (3) u(x,0) = uo(x), ut((x,0) = u1x).
Wydawca
Rocznik
Strony
365--386
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
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
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
  • Department of Mathematics, Can Tho University, Can Tho City, Vietnam
Bibliografia
  • [1] J. Boujot, Alain Pham Ngoc Dinh, J. P. Veyrier, Oscillateurs harmoniques faiblement perturbés: L'algorithme numérique des ''par de géants", RAIRO, Analyse numérique 14 (1980), 3-23.
  • [2] T. Caughey, J. Ellison, Existence, uniqueness and stability of solutions of a class of nonlinear differential equations, J. Math. Anal. Appl. 51 (1975), 1-32.
  • [3] Alain Pham Ngoc Dinh, Sur un problème kyperbolique faiblement non-linéaire à une dimension, Demonstratio Math. 16 (1983), 269-289.
  • [4] Alain Pham Ngoc Dinh, Nguyen Thanh Long, Linear approximation and asymptotic expansion associated to the nonlinear wave equation in one dimension, Demonstratio Math. 19 (1986), 45-63.
  • [5] F. Ficken, B. Fleishman, Initial value problems and time periodic solutions for a nonlinear wave equation, Comm. Pure Appl. Math. 10 (1957), 331-356.
  • [6] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod-Gauthier-Villars, Paris, 1969.
  • [7] Nguyen Thanh Long, Alain Pham Ngoc Dinh, On the quasilinear wave equation: Utt - ∆u + f(u, ut) = 0 associated with a mixed nonhomogeneous condition, Nonlinear Anal. 19 (1992), 613-623.
  • [8] Nguyen Thanh Long, Alain Pham Ngoc Dinh, A semilinear wave equation associated with a linear differential equation with Cauchy data, Nonlinear Anal. 24 (1995), 1261-1279.
  • [9] Nguyen Thanh Long, Tran Ngoc 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] Nguyen Thanh Long, Alain Pham Ngoc Dinh, Tran Ngoc Diem, Linear recursive schemes and symptotic expansion associated with the Kirchhoff-Carrier operator, J. Math. Anal. Appl. 267 (2002), 116-134.
  • [11] E. L. Ortiz, Alain Pham Ngoc Dinh, Linear recursive schemed associated with some nonlinear partial differential equations in one dimensions and the Tau method, SIAM J. Math. Anal 18 (1987), 452-464.
  • [12] P. H. Rabinowitz, Periodic solutions of nonlinear hyperbolic differential equations, Comm. Pure Appl. Math. 20 (1967), 145-205.
  • [13] P. A. Raviart, J. M. Thomas, Introduction à l’analyse numérique des equations aux dérivées partielles, Masson, Paris, 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0013-0011
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