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

• Autorzy: Long N. T. , Tam N. C. , Truc N. T. T.
• 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).

Słowa kluczowe

EN

weak solutions; perturbed problem; linear recurrent sequence

PL

linearne ciągi okresowe; problem zaburzenia; rozwiązania słabe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 365--386
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Long N. T.

• 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

Tam N. C.

• 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

Truc N. T. T.

• 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.