Abstract:
We consider the questions of one value solvability of the inverse problem for a nonlinear partial Fredholm type integro-differential equation of the fourth order with degenerate kernel. The method of degenerate kernel is developed for the case of inverse problem for the considering partial Fredholm type integro-differential equation of the fourth order. After denoting the Fredholm type integro-differential equation is reduced to a system of integral equations. By the aid of differentiating the system of integral equations reduced to the system of differential equations. When a certain imposed condition is fulfilled, the system of differential equations is changed to the system of algebraic equations. For the regular values of spectral parameterthe system of algebraic equations is solved by the Kramer metod. Using the given additional condition the nonlinear Volterra type integral equation of second kind with respect to main unknowing function and the nonlinear Volterra special type integral equation of first kind with respect to restore function are obtained. We use the method of successive approximations combined with the method of compressing maps. Further the restore function is defined. This paper developes the theory of Fredholm integro-differential equations with degenerate kernel.
Keywords:
inverse problem, integro-differential equation, Fredholm type equation, degenerate kernel, system of integral equations, one valued solvability.
Original article submitted 29/IV/2015 revision submitted – 14/VI/2015
Citation:
T. K. Yuldashev, “An inverse problem for a nonlinear Fredholm
integro-differential equation of fourth order with degenerate kernel”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 736–749
\Bibitem{Yul15}
\by T.~K.~Yuldashev
\paper An inverse problem for a nonlinear Fredholm
integro-differential equation of fourth order with degenerate kernel
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 4
\pages 736--749
\mathnet{http://mi.mathnet.ru/vsgtu1434}
\crossref{https://doi.org/10.14498/vsgtu1434}
\zmath{https://zbmath.org/?q=an:06969191}
\elib{https://elibrary.ru/item.asp?id=25687500}
Linking options:
https://www.mathnet.ru/eng/vsgtu1434
https://www.mathnet.ru/eng/vsgtu/v219/i4/p736
This publication is cited in the following 9 articles:
Yu. P. Apakov, S. M. Mamajanov, “Boundary value problem for a fourth-order equation of parabolic-hyperbolic type with multiple characteristics, whose slopes are greater than one”, Russian Math. (Iz. VUZ), 66:4 (2022), 1–11
E. Providas, I. N. Parasidis, “On the solution of some higher-order integro-differential equations of special form”, Vestn. SamU. Estestvennonauchn. ser., 26:1 (2020), 14–22
T. K. Yuldashev, “Ob odnoi nelokalnoi obratnoi zadache dlya nelineinogo integro-differentsialnogo uravneniya Benney-Luke s vyrozhdennym yadrom”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2018, no. 3, 19–41
T. K. Yuldashev, “Nelokalnaya kraevaya zadacha dlya neodnorodnogo psevdoparabolicheskogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 42–54
T. K. Yuldashev, “Ob odnom smeshannom differentsialnom uravnenii chetvertogo poryadka”, Izv. IMI UdGU, 2016, no. 1(47), 119–128
T. K. Yuldashev, “Nonlocal problem for a mixed type differential equation in rectangular domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2016, no. 3, 70–78
Citation in format AMSBIB
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