Mixed value problem for a Boussinesq type integro-differential equation with reflecting deviation and degenerate kernel
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
This article considers the questions of one value solvability of the mixed value problem for a nonlinear Boussinesq type fourth-order integro-differential equation with reflecting deviation argument and degenerate kernel. The method of degenerate kernel is developed for the case of nonlinear Boussinesq type fourthorder partial integro-differential equation. The Fourier method of separation of variables is employed. By denoting the integro-differential equation is reduced to a system of countable system of algebraic equations with complex right-hand side. After solving this system and substituting it into the preceding formula, we obtain the countable system of nonlinear integral equations (CSNIE). To prove the theorem of one value solvability of CSNIE we use the method of successive approximations. Further the article shows the convergence of the obtained Fourier series to the solution of mixed value problem. This paper advances the theory of partial integro-differential equations with degenerate kernel.
Abstract
This article considers the questions of one value solvability of the mixed value problem for a nonlinear Boussinesq type fourth-order integro-differential equation with reflecting deviation argument and degenerate kernel. The method of degenerate kernel is developed for the case of nonlinear Boussinesq type fourthorder partial integro-differential equation. The Fourier method of separation of variables is employed. By denoting the integro-differential equation is reduced to a system of countable system of algebraic equations with complex right-hand side. After solving this system and substituting it into the preceding formula, we obtain the countable system of nonlinear integral equations (CSNIE). To prove the theorem of one value solvability of CSNIE we use the method of successive approximations. Further the article shows the convergence of the obtained Fourier series to the solution of mixed value problem. This paper advances the theory of partial integro-differential equations with degenerate kernel.
참고문헌 (10)
- V. A. Zolotarev, "Direct and inverse problems for an operator with nonlocal potential", Sbornik:Mathem, 203(12), pp.1785~1807 (2012)
- M. O. Korpusov, "Solution blow-up for a class of parabolic equations with double nonlinearity", Sbornik: Mathem, 204(3), pp.323~346 (2013)
- L. S. Pulkina, "A nonlocal problem for a hyperbolic equation with integral conditions of the first kind with time-dependent kernels", Russian Mathematics, 56(10), pp.26~37 (2012)
- K. B. Sabitov, "A boundary value problem for a third order equation of mixed type", Dokl. Math, 80(1), pp.565~568 (2009)
- K. B. Sabitov, "The Dirichlet problem for a third-order equation of mixed type in a rectangular domain", Differ. Equation, 47(5), pp.706~714 (2011)
- J. Hale, "Theory of Functional Differential Equations" (1977), Springer–Verlag
- T. K. Yuldashev, "A certain Fredholm partial integro-differential equation of the third order", Russian Mathematics, 59(9), pp.62~66 (2015)
- T. K. YULDASHEV, "A double inverse problem for a Fredholm partial integro-differential equation of fourth order", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 18(3), pp.417~426 (2015), 장전수학회
- T.K.YULDASHEV, "MIXED VALUE PROBLEM FOR A PSEUDOPARABOLIC TYPE INTEGRO-DIFFERENTIAL EQUATION WITH DELAY AND DEGENERATE KERNEL", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 19(2), pp.309~317 (2016), 장전수학회
- T. K. Yuldashev, "Inverse problem for a nonlinear Benney–Luke type integro-differential equations with degenerate kernel", Russian Mathematics, 60(9), pp.53~60 (2016)