Integral Volterra equations of the first kind, numerical methods, inverse and ill-posed problems
Main publications:
Apartsin A. S. Some ill-posed problems and their applications in energy research // Sov. Tech. Rev. A. Energy, v. 6, part 1, Harwood Academic Publishers GmbH, USA, 1992, p. 65–125.
A. S. Apartsyn, I. V. Sidler, “On the test Volterra equations of the first kind in the integral models of developing systems”, Avtomat. i Telemekh., 2018, no. 4, 31–45; Autom. Remote Control, 79:4 (2018), 604–616
A. S. Apartsyn, E. V. Markova, I. V. Sidler, “Influence of economic indices on the solution to the optimization problem of the age structure of power plants equipment”, Bulletin of Irkutsk State University. Series Mathematics, 25 (2018), 19–32
3.
A. S. Apartsyn, I. V. Sidler, “Study of test Volterra equations of the first kind in integral models of developing systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 24:2 (2018), 24–33
A. S. Apartsyn, E. V. Markova, I. V. Sidler, “Integral model of developing system without prehistory”, Tambov University Reports. Series: Natural and Technical Sciences, 23:123 (2018), 361–367
A. S. Apartsyn, I. V. Sidler, “The test Volterra equation of the first kind in integral models of developing systems containing $n$ age groups”, Tambov University Reports. Series: Natural and Technical Sciences, 23:122 (2018), 168–179
A. S. Apartsin, “To the theory of Volterra integral equations of the first kind with discontinuous kernels”, Zh. Vychisl. Mat. Mat. Fiz., 56:5 (2016), 824–839; Comput. Math. Math. Phys., 56:5 (2016), 810–825
A. S. Apartsin, I. V. Sidler, “Using the nonclassical Volterra equations of the first kind to model the developing systems”, Avtomat. i Telemekh., 2013, no. 6, 3–16; Autom. Remote Control, 74:6 (2013), 899–910
A. S. Apartsin, “Studying the polynomial Volterra equation of the first kind for solution stability”, Avtomat. i Telemekh., 2011, no. 6, 95–102; Autom. Remote Control, 72:6 (2011), 1229–1236
A. S. Apartsyn, “On equivalent norms in the theory of Volterra polinomial equations of the first kind”, Bulletin of Irkutsk State University. Series Mathematics, 3:1 (2010), 19–29
A. S. Apartsyn, V. A. Spiryaev, “On unimprovable Lambert estimates of solutions for one class of nonlinear integral inequalities”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:2 (2010), 3–12
A. S. Apartsyn, M. S. Shcherbinin, “Lambert function and some problems of control in a Lancaster model”, Avtomat. i Telemekh., 2009, no. 4, 48–57; Autom. Remote Control, 70:4 (2009), 605–614
2008
13.
A. S. Apartsyn, “Multilinear Volterra equations of the first kind and some problems of control”, Avtomat. i Telemekh., 2008, no. 4, 3–16; Autom. Remote Control, 69:4 (2008), 545–558
A. S. Apartsyn, “On the convergence of numerical methods for solving a Volterra bilinear equations of the first kind”, Zh. Vychisl. Mat. Mat. Fiz., 47:8 (2007), 1378–1386; Comput. Math. Math. Phys., 47:8 (2007), 1323–1331
A. S. Apartsyn, S. V. Solodusha, “Test signal amplitude optimization for identification of the volterra kernels”, Avtomat. i Telemekh., 2004, no. 3, 116–124; Autom. Remote Control, 65:3 (2004), 464–471
A. S. Apartsyn, “Multilinear volterra equations of the first kind”, Avtomat. i Telemekh., 2004, no. 2, 118–125; Autom. Remote Control, 65:2 (2004), 263–269
A. S. Apartsyn, “On new classes of linear multidimensional equations of the first kind of Volterra type”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 11, 28–41; Russian Math. (Iz. VUZ), 39:11 (1995), 25–37
A. S. Apartsyn, Teng Meng Yan, “Unimprovable estimates of the solutions of certain integral inequalities”, Sibirsk. Mat. Zh., 20:1 (1979), 192–195; Siberian Math. J., 20:1 (1979), 139–141
1975
19.
A. B. Bakushinskii, A. S. Apartsyn, “Methods of stochastic approximation type for the solution of linear ill-posed problems”, Sibirsk. Mat. Zh., 16:1 (1975), 12–18; Siberian Math. J., 16:1 (1975), 9–14
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