Inverse problem for elliptic Fredholm integro-differential equation
T. K. YuldashevA. G. Loskutova1
|It is studied the one value solvability of the nonlinear inverse problem for an elliptic Fredholm integro-differential equation. It is modified the method of degenerate kernel designed for Fredholm integral equations of the second kind. It is obtained nonlinear integral equation of the first kind, which with the aid of special non-classical integral transformation is reduced to a nonlinear integral equation of the second kind. It is used the method of successive approximations, combined it with the method of compressing maps.
|nonlinear inverse problem, equation of elliptic type, integro-differential equation, integral transformation, method of successive approximation
1Associate professor of Higher Mathematics Chair, M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, email@example.com;
2Student of Faculty of Mechanical Engineering and Mechatronics, M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk
Citation: T. K. YuldashevA. G. Loskutova, "[Inverse problem for elliptic Fredholm integro-differential equation]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,16:3 (2014) 87–93 (In Russian)