Solvability of Some Classes of Systems of Dual Integral Equations Involving Fourier Transforms
Tóm tắt
The aim of the present work is to consider the existence and uniqueness problems for some classes of general systems of dual integral equations involving Fourier transforms of generalized functions, which are a generalization of some systems of dual equations encountered in the mixed boundary value problems of mathematical physics and contact problems of elasticity.
Tài liệu tham khảo
Ciaurri, Ó., Guadalupe, J.J., Pérez, M., Varona, J.L.: Solving dual integral equations on Lebesgue spaces. Studia Math 142(2), 253–267 (2000)
Eskin, G.I.: Boundary value problems for elliptic pseudo differential equations. Izdat. “Nauka”, (in Russian) (1973)
Mandal, B.N.: Advances in dual integral equations. Chapman & Hall / CRC Press, Boca Raton (1999). 226 p
Ngok, N.V., Popov, G.Y.a.: Dual integral equations associated with fourier transforms. Ukrainskii matematicheskii Zhurnal 38(2), 188–195 (1986)
Ngoc, N.V.: On the solvability of dual integral equations involving fourier transform. Acta Math. Vietnam. 3(2), 21–30 (1988)
Ngoc, N.V.: Dual integral equations involving Fourier transforms with increasing symbols. Acta Math. Vietnam. 34(3), 305–318 (2009)
Ngoc, N.V., Ngan, N.T.: On some systems of dual integral equations involving fourier transform. Algebraic structures in partial differential equations related to complex and Clifford analysis. In: 17th International Conference on Finite and Infinite Application. Ho Chi Minh Univ. of Edu. Press (2010)
Ngoc, N.V., Ngan, N.T.: Solvability of a system of dual integral equations involving fourier transforms. Vietnam J. Math. 38(4), 467–483 (2010)
Ngoc, N.V., Ngan, N.T.: Solvability of a system of dual integral equations of a mixed boundary value problem for the biharmonic equation in a strip. Acta Math. Vietnam 36(2), 375–396 (2010)
Ufljand, Ja.S.: The Method of Dual Equations in Problems of Mathematical Physics. Izdat. “Nauka” Leningrad. Otdel., Leningrad. (in Russian) (1977)
Ufljand, Ja.S.: Integral transforms in problems of elasticity theory. Izdat. “Nauka” Leningrad. (in Russian) (1967)
Vladimirov, V.S.: Generalized functions in mathematical physics. Moscow. (in Russian) (1979)
Volevich, L.R., Panekh, B.P.: Some spaces of generalized functions and imbedding theorems. Uspekhii Math. Nauk 20(1), 3–74 (1965)
Walton, J.R.: A distributional approach to dual integral equations of Titchmarsh type. SIAM J. Math. Anal. 6(4), 628–643 (1975)