A semilinear wave equation associated with a nonlinear integral equation

• Autorzy: Long N. T. , Thuyet T. M.
• Języki publikacji: EN

Słowa kluczowe

EN

Galerkin method; fixed-point theorems; nonlinear integral equation

PL

metoda Galerkina; integralne równania

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 4
• Strony: 915--938
• Opis fizyczny: Bibliogr. 12 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

Thuyet T. M.

• Department of Mathematics, Statistics and Informatics, University of Economics of Hochiminh City, 179-181 Street 3-2, Dist. 10, Hochiminh City, Vietnam

Bibliografia

• [1] Nguyen Thuc An, Nguyen Dinh Trieu, Shock between absolutely solid body and elastic bar with the elastic viscous fractional resistance at the side, J. Mech. NCSR. Vietnam, XIII (2) (1991), 1-7.
• [2] Dang Dinh Ang, Alain Pham Ngoc Dinh, Mixed problem for some semilinear wave equation with a nonhomogeneous condition, Nonlinear Anal. 12 (1988), 581-592.
• [3] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
• [4] Maitine Bergounioux, Nguyen Thanh Long, Alain Pham Ngoc Dinh, Mathematical model for a shock problem involving a linear viscoelastic bar, Nonlinear Anal. 43 (2001), 547-561.
• [5] Alain Pham Ngoc Dinh, Sur un problème hyperbolique faiblement nonlinéaire en dimension 1, Demonstratio Math. 16 (1983), 269-289.
• [6] 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.
• [7] Alain Pham Ngoc Dinh, Nguyen Thanh Long, The semilinear wave equation associated with a nonlinear boundary, Demonstratio Math. 30 (1997), 557-572.
• [8] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non-linéaires, Dunod-Gauthier-Villars, Paris, 1969.
• [9] Nguyen Thanh Long, Alain Pham Ngoc Dinh, On the quasilinear wave equation: utt - Δu + f(u, ut) = 0 associated with a mixed nonhomogeneous condition, Nonlinear Anal. 19 (1992), 613-623.
• [10] 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.
• [11] 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.
• [12] E. L. Ortiz, Alain Pham Ngoc 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.