This article is cited in 2 scientific papers (total in 2 papers)
Inverse problem for a third order Fredholm integro-differential equation with degenerate kernel
T. K. Yuldashev
M. F. Reshetnev Siberian State Aerospace University, Krasnoyarsk, Russia
It is considered the questions of one value solvability of the inverse problem for a third order nonlinear partial Fredholm type integro-differential equation with degenerate kernel. The method of degenerate kernel for second kind Fredholm integral equations is modified for the case of third order partial Fredholm type integro-differential equation. The Fredholm type integro-differential equation is reduced to a system of algebraic equations. By the aid of additional condition it is obtained a second kind nonlinear Volterra type integral equation with respect to main unknown function and a first kind linear Volterra type integral equation with respect to restore function. It is used the method of compressing maps, which gave us the real method of finding the solutions – the method of successive approximations. Further is defined the restore function.
inverse problem, integro-differential equation, Fredholm type equation, degenerate kernel, system of algebraic equations, one valued solvability.
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T. K. Yuldashev, “Inverse problem for a third order Fredholm integro-differential equation with degenerate kernel”, Vladikavkaz. Mat. Zh., 18:2 (2016), 76–85
Citation in format AMSBIB
\paper Inverse problem for a~third order Fredholm integro-differential equation with degenerate kernel
\jour Vladikavkaz. Mat. Zh.
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T. K. Yuldashev, “Obyknovennoe integro-differentsialnoe uravnenie s vyrozhdennym yadrom i integralnym usloviem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 644–655
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
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