Error estimation for nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space
محورهای موضوعی : History and biography
B. Zamanifar
1
(Department of Mathematics, Hamedan Branch,
Islamic Azad University, Hamedan, Iran)
T. Lotfi
2
(Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran)
کلید واژه: Error estimation, Reproducing kernel method, nonlinear pseudoparabolic equation,
چکیده مقاله :
In this paper we discuss about nonlinear pseudoparabolic equations with nonlocalboundary conditions and their results. An effective error estimation for this method altough has not yet beendiscussed. The aim of this paper is to fill this gap.
[1] T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems. Philos. Trans. R. Soc. Lond. Ser. A, 272 (1220) (1972), 47-78.
[2] A. Bouziani, Solvability of nonlinear pseudoparabolic equation with a nonlocal boundary condition. Analysis 55 (2003), 883-904.
[3] A. Bouziani, Initial-boundary value problems for a class of pseudoparabolic equations with integral boundary conditions. J. Math. Anal. Appl. 291 (2004), 371-386.
[4] P. J. Chen, M. E. Gurtin, On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19 (1968), 614-627.
[5] M. G. Cui, Y. Z. Lin, Nonlinear numerical analysis in the reproducing kernel space. Nova 2009.
[6] D. Q. Dai, H. Yu, Nonlocal boundary problems for a third-order one-dimensional nonlinear pseudoparabolic equation. SIAM J. Nonlinear Anal. 66 (2007), 179-191.
[7] G. V. Demidenko, S. V. Uspenskii, Equations and Systems that are not Solved with Respect to the Highest Derivative. Nauchnaya Kniga, Novosibirsk, 1998, 437-443.
[8] I. E. Egorov, S. G. Pyatkov and S. V. Popov, Nonclassical Operator Di erential Equations. Nauka, Novosibirsk, 2000, 336-342.
[9] A. Favini, A. Yagi, Degenerate Di erential Equations in Banach Spaces. vol. 215, Marcel Dekker, New York, 1999, 313-335.
[10] H. Gajewski, K. Grger, K. Zacharias, Nichtlineare Operatorgleichungen und Operator differential gleichungen. Akademie, Berlin, 1974, 281-293.
[11] E. I. Kaikina, Nonlinear pseudoparabolic type equations on a half-line with large initial data. Nonlinear Anal. 67 (2007), 2839-2858.
[12] A. I. Kozhanov, A.I, An initial-boundary value problem for equations of the generalized Boussinesq equation type with a nonlinear source. Mat. Zametki 65 (1) (1999), 70-75.
[13] Y. Z. Lin, Y. F. Zhou, Solving nonlinear pseudoparabolic equations with nonlocal boundary cnditions in reproducing kernel space. Numer Algor, 52 (2009), 173-189.
[14] X. Y. Li, B. Y. Wu, Error estimation for the reproducing kernel method to solve linear boundary value problems. App. Math, 243 (2013), 10-15.
[15] S. Mesloub, A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation. J. Math. Anal. Appl. 316 (2006), 189-209 .
[16] V. Padron, Effect of aggregation on population recovery modeled by a forward-backward pseudoparabolic equation. Trans. Am. Math. Soc. 356 (7) (2004), 2739-2756.
[17] R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. Amer. Math. Soc., Providence 49 (1997), 278-282.
[18] G. A. Sviridyuk, V. E. Fdorov, Analytic semigroups with kernels, and linear equations of Sobolev type. Sib. Mat. Z. 36 (5) (1995),1130-1145.
