Archive of Issues
Uzbekistan Tashkent
Section  Mathematics 
Title  A boundary value problem for a fourth order partial differential equation with the lowest term 
Author(s)  Amanov D.^{a}, Murzambetova M.B.^{a} 
Affiliations  Institute of Mathematics and Information Technologies, National Academy of Sciences of Uzbekistan^{a} 
Abstract  In this paper we study a boundary value problem for the fourth order partial differential equation with the lowest term in a rectangular domain. For the solution of the problem a priori estimate is obtained. From a priori estimate the uniqueness of the solution of the problem follows. For the proof of the solvability of this problem we use the method of separation of variables. The solvability of this problem is reduced to the Fredholm integral equation of the second kind with respect to unknown function. Integral equation is solved by the method of successive approximations. We find the sufficient conditions for the absolute and uniform convergence of series representing the solution of the problem and the series obtained by differentiation four times with respect $x$ and two times with respect to $t$. 
Keywords  boundary value problem, a priori estimate, regular solvability, Fredholm integral equation of the second kind, resolvent, method of successive approximations 
UDC  517.95 
MSC  35G15, 35D05 
DOI  10.20537/vm130101 
Received  30 November 2012 
Language  Russian 
Citation  Amanov D., Murzambetova M.B. A boundary value problem for a fourth order partial differential equation with the lowest term, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 310. 
References 

Full text 