Tytuł artykułu
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We study the initial-boundary value problem for a nonlinear wave equation given by [...] where p > 2, q > l, K, lambda are given constants and uo, u1, F are given functions, the unknown function u(x,t) and the unknown boundary value P (t) satisfy the following nonlinear integral equation [...] where K1, alpha, beta are given constants and g, k arę given functions. In Part 1 we prove a theorem of existence and uniqueness of a weak solution (u, P) of problem (1), (2). The proof is based on the Faedo-Galerkin method associated with a priori estimates, weak convergence and compactness techniques. In Part 3 we obtain an asymptotic expansion of the solution (u, P) of the problem (1), (2) up to order N+1 in three small parameters K, lambda, K1.
Wydawca
Czasopismo
Rocznik
Tom
Strony
85--108
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
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, longnt@hcmc.netnam.vn
Bibliografia
- [1] D. D. Ang, A. P. N. Dinh, Mixed problem for same semilinear wave equation with a nonhomogeneous condition, Nonlinear Anal. 12 (6) (1988), 581-592.
- [2] N. T. An, N. D. Trieu, Shock between absolutely solid body and elastic bar with the elastic viscous frictional resistance at the side, J. Mech. NCSR.Yietnam 13 (2) (1991), 1-7.
- [3] M. Bergounioux, N. T. Long, A. P. N. Dinh, Mathematical model for a shock problem involving a linear viscoelastic bar, Nonlinear Anal. 43 (5) (2001), 547-561.
- [4] F. E. Browder, On nonlinear wave equations, Math. Z. 80 (1962), 249-264.
- [5] E. L. A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, 1955, p. 43.
- [6] J. L. Lions, W. A. Strauss, Some nonlinear evolution equationtions, Bull. Soc. Math., Fiance, 93 (1965), 43-96.
- [7] J. L. Lions, Equations differentielles operationelles et problemes aux limites, Springer-Verlag, Berlin, 1961, p. 96, Section 7.
- [8] J. L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod; Gauthier-Villars, Paris, 1969.
- [9] N. T. Long, A. P. N. Dinh, T. N. Diem, On a shock problem involving a nonlinear viscoelastic bar, J. Boundary Value Problems, Hindawi Publishing Corporation, 2005 (3) (2005), 337-358.
- [10] N. T. Long, L. V. Ut, N. T. T. Truc, On a shock problem involving a linear viscoelastic bar, Nonlinear Anal. 63 (2) (2005), 198-224.
- [11] N. T. Long, V. G. Giai, A wave equation associated with mixed nonhomogeneous conditions: Global existence and asymptotic expansion of solutions, Nonlinear Anal. 66 (7) (2007), 1526-1546.
- [12] N. T. Long, L. X. Truong, Existence and asymptotic espansion for a mscoelastic problem with a mixed nonhomogeneous condition, Nonlinear Anal. 67 (3) (2007), 842-864.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0047-0009