https://oldena.lpnu.ua/handle/ntb/52524| Title: | Inverse Problem for Two-Dimensional Heat Equation with an Unknown Source |
| Authors: | Pabyrivska, Nelya Pabyrivskyy, Viktor |
| Affiliation: | Lviv Politechnic National University |
| Bibliographic description (Ukraine): | Pabyrivska N. Inverse Problem for Two-Dimensional Heat Equation with an Unknown Source / Nelya Pabyrivska, Viktor Pabyrivskyy // Data stream mining and processing : proceedings of the IEEE second international conference, 21-25 August 2018, Lviv. — Львів : Lviv Politechnic Publishing House, 2018. — P. 361–363. — (Hybrid Systems of Computational Intelligence). |
| Bibliographic description (International): | Pabyrivska N. Inverse Problem for Two-Dimensional Heat Equation with an Unknown Source / Nelya Pabyrivska, Viktor Pabyrivskyy // Data stream mining and processing : proceedings of the IEEE second international conference, 21-25 August 2018, Lviv. — Lviv Politechnic Publishing House, 2018. — P. 361–363. — (Hybrid Systems of Computational Intelligence). |
| Is part of: | Data stream mining and processing : proceedings of the IEEE second international conference, 2018 |
| Conference/Event: | IEEE second international conference "Data stream mining and processing" |
| Issue Date: | 28-Feb-2018 |
| Publisher: | Lviv Politechnic Publishing House |
| Place of the edition/event: | Львів |
| Temporal Coverage: | 21-25 August 2018, Lviv |
| Keywords: | inverse problem Green function Volterra integral equations unknown source |
| Number of pages: | 3 |
| Page range: | 361-363 |
| Start page: | 361 |
| End page: | 363 |
| Abstract: | The paper establishes existence and unique conditions for an inverse problem with an unknown source. The unknown source is a polynom for two spatial variables with unknown coefficients depending on time. |
| URI: | https://ena.lpnu.ua/handle/ntb/52524 |
| ISBN: | © Національний університет „Львівська політехніка“, 2018 © Національний університет „Львівська політехніка“, 2018 |
| Copyright owner: | © Національний університет “Львівська політехніка”, 2018 |
| References (Ukraine): | [1] E. Savateev, “The problem of identification of a coefficient in a parabolic equation,” Siberian Mathematical Journal. vol.36, no. 1. pp. 177-185, 1995. [2] M. Ivanchov, “Inverse problem for the multidimensional heat equation with unknown source,” Matematychni Studii. no16, pp. 93-98, 2001. [3] Dinh Nho Hào, Phan Xuan Thanh, D. Lesnic, and M. Ivanchov, “Determination of a source in the heat equation from integral observations,” Journal of Computational and Applied Mathematics, no. 264, pp. 82–98, 2014. [4] M. S. Hussein, and D. Lesnic, “Simultaneous determination of timedependent coefficients and heat source,” International Journal for Computational Methods in Engineering Science and Mechanics, vol. 17, pp. 401-411, August 2016. [5] N. Protsakh, “Inverse problem for weakly nonlinear ultraparabolic equation with three unknown functions of different arguments on the right side,” Ukrainian Mathematical Journal. vol. 66, no. 3, pp. 371-390, 2014. [6] K. Kasemets, and J. Janno, “Reconstruction of a Source Term in a Parabolic Integro-Differential Equation from Final Data,” Mathematical Modelling and Analysis, vol. 16, no. 2, pp.199–219, 2011. [7] M. Hussein, D. Lesnic, and M. Ivanchov, “Identification of a Heterogeneous Orthotropic Conductivity in a Rectangular Domain,” International Journal of Novel Ideas: Mathematics, S.l., vol. 1, pp. 1-11, apr. 2017. [8] N. Pabyrivska, and V. Vlasov, “The determination of major coefficient factor in parabolic equation,” Mathematical methods and physico-mechanical fields, vol.49, no. 3, pp.18-25, 2006. [9] N. Pabyrivska, and O. Varenyk, “The determination of major coefficient factor in parabolic equation,” Lviv University Paper. Ed.64,. pp.181-189. [10] M. Ivanchov, Inverse problem for equations of parabolic type. Mathematical Studies. Monograph Series. Lviv. VNTL Publishers. vol.10, 2003. [11] A. Hasanov, “Simultaneus determination of source terms in liner parabolic problem from the final overdetermination approach,” J. Math. Anal.Appl., vol. 330(2) pp. 766-779, 207. Doi:10.1016/j.jmaa.2006.08.018. [12] A. Lorenzi and G. Mola, “Identefication of unknown terms in convolution integro-differential equations in a Banach space,” J.Inverse Ill-Posed Probl., vol. 18(3), pp. 321-355, 2010. Doi:10.1515/jllp.2010.016. [13] E. Pais, “Identification of memory kernels in heat flow measuring heat flux at the ends of the bar,” Math. Model. Anal., vol. 15(4), pp. 473-490, 2010. Doi:10.3846/1392-6292.2010.15.473-490. |
| References (International): | [1] E. Savateev, "The problem of identification of a coefficient in a parabolic equation," Siberian Mathematical Journal. vol.36, no. 1. pp. 177-185, 1995. [2] M. Ivanchov, "Inverse problem for the multidimensional heat equation with unknown source," Matematychni Studii. no16, pp. 93-98, 2001. [3] Dinh Nho Hào, Phan Xuan Thanh, D. Lesnic, and M. Ivanchov, "Determination of a source in the heat equation from integral observations," Journal of Computational and Applied Mathematics, no. 264, pp. 82–98, 2014. [4] M. S. Hussein, and D. Lesnic, "Simultaneous determination of timedependent coefficients and heat source," International Journal for Computational Methods in Engineering Science and Mechanics, vol. 17, pp. 401-411, August 2016. [5] N. Protsakh, "Inverse problem for weakly nonlinear ultraparabolic equation with three unknown functions of different arguments on the right side," Ukrainian Mathematical Journal. vol. 66, no. 3, pp. 371-390, 2014. [6] K. Kasemets, and J. Janno, "Reconstruction of a Source Term in a Parabolic Integro-Differential Equation from Final Data," Mathematical Modelling and Analysis, vol. 16, no. 2, pp.199–219, 2011. [7] M. Hussein, D. Lesnic, and M. Ivanchov, "Identification of a Heterogeneous Orthotropic Conductivity in a Rectangular Domain," International Journal of Novel Ideas: Mathematics, S.l., vol. 1, pp. 1-11, apr. 2017. [8] N. Pabyrivska, and V. Vlasov, "The determination of major coefficient factor in parabolic equation," Mathematical methods and physico-mechanical fields, vol.49, no. 3, pp.18-25, 2006. [9] N. Pabyrivska, and O. Varenyk, "The determination of major coefficient factor in parabolic equation," Lviv University Paper. Ed.64,. pp.181-189. [10] M. Ivanchov, Inverse problem for equations of parabolic type. Mathematical Studies. Monograph Series. Lviv. VNTL Publishers. vol.10, 2003. [11] A. Hasanov, "Simultaneus determination of source terms in liner parabolic problem from the final overdetermination approach," J. Math. Anal.Appl., vol. 330(2) pp. 766-779, 207. Doi:10.1016/j.jmaa.2006.08.018. [12] A. Lorenzi and G. Mola, "Identefication of unknown terms in convolution integro-differential equations in a Banach space," J.Inverse Ill-Posed Probl., vol. 18(3), pp. 321-355, 2010. Doi:10.1515/jllp.2010.016. [13] E. Pais, "Identification of memory kernels in heat flow measuring heat flux at the ends of the bar," Math. Model. Anal., vol. 15(4), pp. 473-490, 2010. Doi:10.3846/1392-6292.2010.15.473-490. |
| Content type: | Conference Abstract |
| Appears in Collections: | Data stream mining and processing : proceedings of the IEEE second international conference |
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2018_Pabyrivska_N-Inverse_Problem_for_361-363.pdf | 107.28 kB | Adobe PDF | View/Open | |
| 2018_Pabyrivska_N-Inverse_Problem_for_361-363__COVER.png | 506.95 kB | image/png | View/Open |
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