Inverse problem for a partial difference equation of the higher order
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초록
In this article is proposed the method of studying the inverse problem for a nonlinear partial difference equation with difference hyperbolic operator of the arbitrary natural power. In solving this inverse problem with respect to the restore function is obtained the nonlinear summary equation of the first kind, which is reduced by the aid of special nonclassical summary transform into nonlinear summary equation of the second kind. Further is used the method of successive approximations combined with the method of compressing maps. It is proved the theorem of existence and uniqueness of solution of the considering inverse problem.
Abstract
In this article is proposed the method of studying the inverse problem for a nonlinear partial difference equation with difference hyperbolic operator of the arbitrary natural power. In solving this inverse problem with respect to the restore function is obtained the nonlinear summary equation of the first kind, which is reduced by the aid of special nonclassical summary transform into nonlinear summary equation of the second kind. Further is used the method of successive approximations combined with the method of compressing maps. It is proved the theorem of existence and uniqueness of solution of the considering inverse problem.
참고문헌 (7)
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- A. A. Samarsky, "Introduction to numerical methods" (1987), Nauka
- T. K. Yuldashev, "On a nonlinear system of functional difference equations with nonlinear complicated mixed maxima", Advanced Studies in Contemporary Mathematics, 13(1), pp.1~4 (2006), 장전수학회
- T. K. YULDASHEV, "ON A FIRST ORDER QUASILINEAR PARTIAL DIFFERENCE EQUATION", Advanced Studies in Contemporary Mathematics, 23(4), pp.677~680 (2013), 장전수학회
- T. K. Yuldashev, "On a summary equation with weak nonlinear right-hand side", Advanced Studies in Contemporary Mathematics, 15(1), pp.95~98 (2007), 장전수학회
- T. K. Yuldashev, "On a solvability of nonlinear evolution summary equations with nonlinear deviation", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 11(1), pp.83~88 (2008), 장전수학회
- T.K.YULDASHEV, "On a solvability of nonlinear summary equation of the third kind", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 16(1), pp.151~155 (2013), 장전수학회