Geodesic
Numerical solution to parametric identification problems for partial differential equations
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2018), pp. 33-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper proposes a numerical method for solving the problem, based on the use of the method of lines to reduce the problem to a system of ordinary differential equations with unknown parameters. Next, we use a special representation of the solution of the obtained boundary value problem for a linear system of differential equations with nonlocal conditions, by means of which the problem of parametric identification reduces to solving auxiliary boundary value problems and a system of algebraic equations. It is important to note that, unlike optimization approaches, The construction of any iterative procedures or minimizing sequences is used.
Keywords: inverse problem, method of lines, parametric identification.
Mots-clés : parabolic type equation 
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     author = {V. M. Abdullayev},
     title = {Numerical solution to parametric identification problems for partial differential equations},
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     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_2_a3/}
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V. M. Abdullayev. Numerical solution to parametric identification problems for partial differential equations. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2018), pp. 33-44. http://geodesic.mathdoc.fr/item/VKAM_2018_2_a3/

[1] Kamynin V. L., “Ob obratnoj zadache opredelenija pravoj chasti v parabolicheskom uravnenii s usloviem integral'nogo pereopredelenija”, Matem. Zametki, 2005 vol 77, no. 4, 522–534 | DOI | Zbl

[2] Belov Yu. Ya., “Inverse problems for parabolic equations”, J. Inv. Ill Posed Problems. 1:4 (1993), 283–305 | DOI | MR | Zbl

[3] Sergienko I. B., Dejneka V. S., “Reshenie nekotoryh obratnyh zadach teploprovodnosti dlja sostavnoj plastiny s ispol'zovaniem psevdoobratnyh matric”, Doklady NAN Ukrainy, 2011, no. 12, 28–34 | Zbl

[4] Hasanov A., Otelbaev M., Akpayev B., “Inverse heat conduction problems with boundary and final time measured output data”, Inverse Probl. Sci. Eng.. 19 (2011), 895–1006 | MR

[5] Ivanchov M.İ., “Inverse problems for the heat-conduction equation with nonlocal boundary conditions”, Ukrainian Mathematical Journal, 45:8 (1993), 1186–1192 | DOI | MR | Zbl

[6] Savateev E. G., “O zadache identifikacii kojefficienta parabolicheskogo uravnenija”, Sib. matem. zhurn. 1995, 36:1, 177–185 | Zbl

[7] Prilepko A. I., Kostin A. B., “O nekotoryh obratnyh zadachah dlja parabolicheskih uravnenij s final'nym i integral'nym nabljudeniem”, Matem. sb., 183:4 (1992), 49–68 | MR | Zbl

[8] Yan L, Fu C.L, Yang F.L., “The method of fundamental solutions for the inverse heat source problem”, Eng. Anal. Boundary Elements, 32 (2008), 216–222 | DOI | Zbl

[9] Ismailov M. I, Kanca F, Lesnic D., “Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions”, Appl. Math. Comput., 218 (2011), 4138–4146 | MR | Zbl

[10] Cannon J.R, Duchateau P., “Structural identification of an unknown source term in a heat equation”, Inverse Probl., 14 (1998), 535–551 | DOI | MR | Zbl

[11] Aida-zade K.R., Abdullayev V.M., “Solution to a class of inverse problems for system of loaded ordinary differential equations with integral conditions”, J. Inv. Ill Posed Problems, 24:5 (2016), 543-558 | DOI | MR | Zbl

[12] Abdullayev V. M. , Aida-zade K. R., “Optimization of loading places and load response functions for stationary systems”, Comput. Math. Math. Phys., 57:4 (2017), 634–644 | DOI | MR | Zbl

[13] Abdullaev V. M. , Aida-zade K. R., “On the numerical solution of loaded systems of ordinary differential equations”, Comput. Math. Math. Phys., 44:9 (2004), 1505–1515 | MR | Zbl

[14] Aida-zade K.R., “A Numerical method of restroring the parameters of a dynamic system”, Cybern. Syst. Analysis., 40:3 (2004), 392–399 | DOI | MR | Zbl