Сиппаттамалары еселi диффененциалдық теңдеулердегi параметрдi қалпына келтiрудiң керi есебi
DOI:
https://doi.org/10.26577/JMMCS.2022.v113.i1.01Аннотация
Керi есептер - белгiлi немесе берiлген әсерлердiң себептерiн табу мәселесi. Олар бiздi қызықтыратын объектiнiң сипаттамалары тiкелей бақылау үшiн қол жетiмдi болмаған кезде пайда болады. Бұл, мысалы, кейбiр нүктелердегi олардың белгiленген мәндерiне сәйкес өрiс көздерiнiң сипаттамаларын қалпына келтiру, белгiлi шығыс сигналынан бастапқы сигналды қалпына келтiру немесе интерпретациялау және т.б. Берiлген жұмыста бiз дифференциалдық теңдеуге қойылған керi есептiң шешiмдiлiгiн зерттеймiз. Жұмыс бiрнеше сипаттамалары бар үшiншi реттi дифференциалдық теңдеулер үшiн сызықты емес керi коэффициенттi есептерiнiң Соболев кеңiстiгiнде шешiмдiлiгiн зерттеуге арналған. Бұл мақалада белгiлi бiр дифференциалдық теңдеудiң шешiмiн iздеумен қатар теңдеудiң бiр немесе бiрнеше коэффициенттерiн табу да талап етiледi, сондықтан оларды керi коэффициенттiк есептер деп атаймыз. Бұл жұмыста зерттелген есептердiң айрықша ерекшелiгi белгiсiз коэффициент белгiлi бiр тәуелсiз айнымалылардың функциясы емес, сандық параметр болып табылады.
Библиографиялық сілтемелер
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[3] Anikonov, Yu.E. Inverse and Ill–Posed Problems. Utrecht: VSP, 1999
[4] Kozhanov, A. I. Composite Type Equations and Inverse Problems. Utrecht: VSP, 1999.
[5] Lorenzi, A. Introduction to Identification Problems via Functional Analysis. Utrecht: VSP, 2001.
[6] Anikonov, Yu.E. Inverse Problems for Kinetic and Other Evolution Equation. Utrecht: VSP, 2001.
[7] Danilaev, P.G. Coefficient Inverse Problems for Parabolic Type Equations and Their Applications. Utrecht: VSP, 2001.
[8] Belov, Yu.Ya. Inverse Problems for Partial Differntial Equations. Utrecht: VSP, 2002.
[9] Lavrentiev, M.M. Inverse Problems of Mathematical Physics. Utrecht: VSP, 2003.
[10] Megrabov, A.G. Forward and Inverse Problems for Hyperbolic, Elliptic and Mixed Type Equations. Utrecht: VSP, 2003.
[11] Ivanchov, M. Inverse Problems for Equations of Parabolic Type. Lviv: WNTL Publishers, 2003.
[12] Romanov V. G. Stability in inverse problems. Moscow: Nauchny mir, 2005.(In Russian)
[13] Isakov, V. Inverse Problem for Partial Differential Equations. Springer Verlag, 2009.
[14] Kabanikhin S. I. Inverse and ill-posed problems. Novosibirsk: Siberian Book Publishing House. 2009. (In Russian)
[15] Hasanov, H.A., Romanov, V.G. Introduction to Inverse Problems for Differential Equations; Springer: New York, NY, USA, 2017.
[16] Vatulyan A. O. Coefficient inverse problems of mechanics. Moscow: Fizmatlit, 2019.(In Russian)
[17] Kozhanov A. I. On the definition of sources in the linearized Kortweg-de Vries equation. Math. notes of YSU. 2002. Vol. 9, vol. 2. P. 74-82.(In Russian)
[18] Kozhanov A. I. On solvability of some nonlinear inverse problems for a single equation with multiple characteristics. Vestnik NSU, series: mathematics, mechanics, Informatics. 2003. Vol. 3, issue. 3. P. 34-51.(In Russian)
[19] Kozhanov A. I. Inverse problem for equations with multiple characteristics: the case of the unknown coefficient is timedependent. The reports of the Adyghe (Circassian) international Academy of Sciences. 2005. Vol. 8, No. 1. P. 38-49.(In Russian)
[20] Lorenzi, A. Recovering Two Constans in a Linear Parabolic Equation. Inverse Problems in Applied Sciences. J. Phys. Conf. Ser. 2007, 73, 012014.
[21] Lyubanova, A.S. Identification of a Constant Coefficient in an Elliptic Equation. Appl. Anal. 2008, 87, 1121–1128.
[22] Lorenzi, A.; Mola, G. Identification of a Real Constant in Linear Evolution Equation in a Hilbert Spaces. Inverse Probl. Imaging. 2011, 5, 695–714.
[23] Mola, G. Identification of the Diffusion Coefficient in Linear Evolution Equation in a Hilbert Spaces. J. Abstr. Differ. Appl. 2011, 2, 18–28.
[24] Lorenzi, A.; Mola, G. Recovering the Reaction and the Diffusion Coefficients in a Linear Parabolic Equations. Inverse Probl. 2012, 28, 075006.
[25] Mola, G.; Okazawa, N.; Pru?ss, J.; Yokota, T. Semigroup–Theoretic Approach to Identification of Linear Diffusion Coefficient. Discret. Contin. Dyn. Syst. S. 2016, 9, 777–790.
[26] Kozhanov, A.I.; Safiullova, R.R. Determination of Parameter in Telegraph Equation. Ufa Math. J. 2017, 9, 62–75.
[27] Kozhanov, A.I. Inverse Problems of Finding of Absorption Parameter in the Diffusion Equation. Math. Notes. 2019, 106, 378–389.
[28] Kozhanov, A.I. The Heat Transfer Equation with an Unknown Heat Capacity Coefficient. J. Appl. Ind. Math. 2020, 14, 104–114. 15
[29] Kozhanov, A. I. Hyperbolic Equations with Unknown Coefficients Symmetry. 2020. V. 12. Issue 9. 1539.
[30] V. S. Vladimirov, equations of mathematical physics. M.: Nauka, 1974.
[31] Courant, R. Partial Differential Equations. New York–London, 1962.
[32] Sobolev, S.L. Some Applications of Functional Analysis in Mathematical Physics, Providence: Amer. Math. Soc., 1991.
[33] Ladyzhenskaya O.A., Uraltseva N.N. Linear and Quasilinear Elliptic Equations, New York and London: Academic Press, 1987.
[34] Triebel, H. Interpolation Theory, Function Spaces, Differential Operators. North–Holland Publ., Amsterdam, 1978.
[35] Dzhenaliev M. T. To the theory of linear boundary value problems for loaded differential equations. Almaty. Institute of theoretical and applied mathematics, 1995.(In Russian)
[36] Nakhushev a.m. Loaded equations and their application. Moscow: Nauka. 2012 (In Russian)
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Как цитировать
Kozhanov, A. I., Abylkayrov, U. U., & Ashurova, G. (2022). Сиппаттамалары еселi диффененциалдық теңдеулердегi параметрдi қалпына келтiрудiң керi есебi. Қазұу Хабаршысы. Математика, механика, информатика сериясы, 113(1). https://doi.org/10.26577/JMMCS.2022.v113.i1.01
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