coefficient inverse problems for hyperbolic equations, minimization of misfit functional.
Subject:
Creation of numetical methods for solution of coefficient inverse problems for hyperbolic equations and systems.
Main publications:
A. L. Karchevsky, V. G. Yakhno. One-dimensional inverse problems for systems of elasticity with a source of explosive type // Journal of Inverse and Ill-Posed Problems, VSP, The Netherlands, v. 7, no. 4, 1999, p. 347–364.
A. L. Karchevsky. Properties of the misfit functional for a nonlinear one-dimentioanal coefficient hyperbolic inverse problem // Journal of Inverse and Ill-posed Problems, VSP, The Netherlands, v. 5, no. 2, 1997, p. 139–163.
N. E. Sibiryakov, D. Yu. Kochkin, O. A. Kabov, A. L. Karchevsky, “Determination of the heat flux density in the region of the contact line during evaporation of a liquid into a bubble”, Sib. Zh. Ind. Mat., 26:3 (2023), 95–111; J. Appl. Industr. Math., 17:3 (2023), 628–639
2022
2.
G. M. Mitrofanov, A. L. Karchevsky, “Mathematical modeling for thin-layered elastic media in seismic exploration”, Sib. Zh. Ind. Mat., 25:3 (2022), 120–134
2021
3.
A. L. Karchevsky, L. A. Nazarova, L. A. Nazarov, “Method for determining the filtration properties of a fractured porous reservoir by solving the inverse problem using well output measurements”, Prikl. Mekh. Tekh. Fiz., 62:6 (2021), 74–80; J. Appl. Mech. Tech. Phys., 62:6 (2021), 952–958
A. L. Karchevsky, “Analytical solutions to the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for the boundary conditions of various types”, Sib. Zh. Ind. Mat., 23:4 (2020), 48–68; J. Appl. Industr. Math., 14:4 (2020), 648–665
A. L. Karchevsky, “Solution of the convolution type Volterra integral equations
of the first kind by the quadrature-sum method”, Sib. Zh. Ind. Mat., 23:3 (2020), 40–52; J. Appl. Industr. Math., 14:3 (2020), 503–512
V. A. Dedok, A. L. Karchevsky, V. G. Romanov, “A numerical method of determining permittivity from the modulus of the electric intensity vector of an electromagnetic field”, Sib. Zh. Ind. Mat., 22:3 (2019), 48–58; J. Appl. Industr. Math., 13:3 (2019), 436–446
V. G. Romanov, A. L. Karchevsky, “Determination of permittivity and conductivity of medium in a vicinity of a well having complex profile”, Eurasian Journal of Mathematical and Computer Applications, 6:4 (2018), 62–72
8.
A. L. Karchevsky, V. A. Dedok, “Reconstruction of permittivity from the modulus of a scattered electric field”, Sib. Zh. Ind. Mat., 21:3 (2018), 50–59; J. Appl. Industr. Math., 12:3 (2018), 470–478
A. L. Karchevsky, Y. M. Turganbayev, S. G. Rakhmetullina, ZH. T. Beldeubayeva, “Numerical solution of an inverse problem of determining the parameters of a source of groundwater pollution”, Eurasian Journal of Mathematical and Computer Applications, 5:1 (2017), 53–73
10.
A. L. Karchevsky, “Determination the possibility of a rock burst in a coal seam”, Sib. Zh. Ind. Mat., 20:4 (2017), 35–43; J. Appl. Industr. Math., 11:4 (2017), 527–534
A. L. Karchevskii, “Calculation of stresses in a coal seam in presence of gas diffusions”, Sib. Zh. Ind. Mat., 19:4 (2016), 31–43; J. Appl. Industr. Math., 10:4 (2016), 482–493
A. L. Karchevsky, B. R. Rysbaiuly, “Analytical expressions for a solution of convective heat and moisture transfer equations in the frequency domain for layered media”, Eurasian Journal of Mathematical and Computer Applications, 3:4 (2015), 55–67
13.
A. L. Karchevskii, L. A. Nazarov, L. A. Nazarova, “Calculation of gas pressure in a closed vessel with coal slack under isothermal desorption”, Sib. Zh. Ind. Mat., 18:1 (2015), 45–55; J. Appl. Industr. Math., 9:2 (2015), 196–205
L. A. Nazarova, L. A. Nazarov, A. L. Karchevsky, M. Vandamme, “Estimation of the diffusion-capacitive parameters of a coal bed by the data of gas pressure measuring in a borehole based on inverse problem solving”, Sib. Zh. Ind. Mat., 17:1 (2014), 78–85; J. Appl. Industr. Math., 8:2 (2014), 267–273
A. L. Karchevsky, “Reformulation of an universe problem statement that reduces computational costs”, Eurasian Journal of Mathematical and Computer Applications, 1:2 (2013), 4–20
16.
A. A. Duchkov, A. L. Karchevskii, “Determination of a terrestrial heat flow from temperature measurements in bottom sediments”, Sib. Zh. Ind. Mat., 16:3 (2013), 61–85; J. Appl. Industr. Math., 7:4 (2013), 480–502
L. A. Nazarov, L. A. Nazarova, A. L. Karchevskii, A. V. Panov, “Estimation of stresses and deformation properties of rock masses based on the solution of an inverse problem by the data of the measurement of free surface displacement”, Sib. Zh. Ind. Mat., 15:4 (2012), 102–109; J. Appl. Industr. Math., 7:2 (2013), 234–240
A. L. Karchevsky, “Reconstruction of pressure and shear velocities and boundaries of thin layers in a thinly stratified layer”, Sib. Zh. Vychisl. Mat., 15:1 (2012), 67–82; Num. Anal. Appl., 5:1 (2012), 54–67
A. L. Karchevsky, “The correct flow chart for numerical solving of an inverse problem by the optimization method”, Sib. Èlektron. Mat. Izv., 5 (2008), 609–619
A. L. Karchevsky, “A correct flow chart for numerical solution to an inverse problem by optimization method”, Sib. Zh. Vychisl. Mat., 11:2 (2008), 139–149; Num. Anal. Appl., 1:2 (2008), 114–122
A. L. Karchevsky, “Algorithm for reconstruction of the elastic constants of an anisotropic layer lying in an isotropic horizontally stratified medium”, Sib. Èlektron. Mat. Izv., 4 (2007), 20–51
A. L. Karchevsky, A. G. Fatianov, “Numerical solution of the inverse problem for a system of elasticity with the aftereffect for a vertically inhomogeneous medium”, Sib. Zh. Vychisl. Mat., 4:3 (2001), 259–268
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