Existence of solutions for one-dimensional wave equations with nonlocal conditions

Electronic Journal of Differential Equations

Volumn 2001, Issue , 2001, Pages

  Beilin, Sergei A ^a  

^a SAMARA NATIONAL RESEARCH UNIVERSITY   (Russian Federation)

Author keywords

Mixed problem; Non local conditions; Wave equation

Indexed keywords

EID: 52549098931     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. A. V. Bitzadze, Urawnenija matematicheskoj fiziki, M.,"Nauka", 1976.
2. A. Bouziani, On a class of parabolic equations with nonlocal boundary conditions, Bulleti de la Classe des Sciences, Académie Royale de Belgique, T.X, 1999, p. 61-77.
3. A. Bouziani, Solution forte d'un problème mixte avec conditions non locales pour une classe d'équations hyperboliques, Bulletin de la Classe des Sciences, Académie Royale de Belgique, T. VIII, 1997, p. 53-70.
4. J. R. Cannon, The solution of the heat equation subject to specification of energy. Quart.Appl. Math., 21, n2, 155-160, 1963.
5. D. G. Gordeziani, G. A. Avalishvili, On the constructing of solutions of the nonlocal initial boundary problems for one-dimentional medium oscillation equations, Matem. Modelirovanie, 12, N. 1, 2000, 94-103.
6. I. S. Gradshtein, I. M. Ryzhik, Tables of integrals, sums, series and products, M., 1963.
7. A. K. Gushin, V. P. Mikhailov, On solvability of nonlocal problems for second-odered ellipti equation, Matem. Sbornik, V. 185, 1994, p. 121-160.
8. V. A. Ilyin, Necessary and sufficient properties of being a basis of a subsystem of eigenfunctions and adjoint functions for Keldysh bundle for odrinary differential operators, Doklady Acad. Nauk SSSR, 227, N. 4, 1976, p. 796-799.
9. N. I. lonkin, Solutions of boundary value problem in heat conductions theory with nonloca boundary conditions, Différents. Uravn., Vol. 13, N2, 1977, p. 294-304.
10. L. I. Kamynin, A boundary value problem in the theory of the heat conduction with nonclas- sical boundary condition, Z. Vychisl. Mat. Fiz., 4, N6, 1964, p. 1006-1024.
11. M. V. Keldysh, On eigenvalues and eigenfunctions of certain classes of not self-adjoint equations, Doklady Acad. Nauk SSSR, 87, 1951, p. 11-14.
12. S. Mesloub, A. Bouziani, On a class of singular hyperbolic equation with a weighted integra condition, Internat. J. Math. & Math. Sci., Vol. 22, No. 3, 1999, pp. 511-519.
13. B. P. Paneiah, On certain nonlocal boundary problemsfor linear differential operators, Matem. zametki., 1984, v. 35, N.3, p. 425-434.
14. L. S. Pulkina, A nonlocal problem with integral conditions for hyperbolic equations, Electron. J. Ddiff. Eqns., Vol. 1999(1999), No. 45, 1-6.
15. L. S. Pulkina, On solvability in L% of nonlocal problem with integral conditions for a hyperbolic equation, Différents. Uravn., V. N. 2, 2000.
16. A. A. Samarskii, Some problems in differential equations theory, Différents. Uravn., Vol. 16, nil, 1980, p. 1221-1228.
17. A. L. Skubachevski, G. M. Steblov, On spectrum of differential operators with domain nondense in Li, Dokladi AN USSR, 1991. v. 321, N.6, p. 1158-1163.
18. N. I. Yurchuk, Mixed problem with an integral condition for certain parabolic equations, Différents. Uravn., Vol. 22, N. 12, 1986, p. 2117-2126.