Differential equations with singularities and of fractional order, potential theory,
differential equations in probability theory,
fractional calculus, special functions
Biography
Graduated from the Department Mathematics of Voronezh State University (VSU) in 1953. The M.Sc. thesis was supervised by prof. O. M. Penkin. In 2004?06, taught in the Department of the Higher Mathematics of the Voronezh State Technological Academy (VSTA). Simultaneously, was a postgraduate student under supervision by prof. L. N. Lyakhov (2004?06). Defended the Ph.D. thesis in 2006. Since August 2006, taught first in "Quality Control and Machine-Building Technology Department" VSTA, since February 2008 in the mathematical department of the Voronezh State Forestry Engineering Academy. Simultaneously, since 2007 have taught in the Department of the Differential Equations of the VSU. Gave many talks on mathematical seminars and conferences in Russia and abroad.
Main publications:
Lyakhov L. N., Shishkina E. L., “Generalized Riesz B-Potentials of the Mixed Type”, Doklady Mathematics, 73:1 (2006), 42–45; Original Russian Text: L. N. Lyakhov, E. L. Shishkina, Doklady Akademii Nauk, 406:3 (2006), 303–307
Shishkina E. L., “Weighting Distribution $r^\lambda$”, Proceeding of Voronezh State University Series: Phisics, Mathematics, 2006, № 1, 215–221
Lyakhov L. N., Shishkina E. L., “General B-Hypersingular Integrals with Homogeneous Characteristic”, Doklady Mathematics, 75:1 (2007), 39–43; Original Russian Text: L. N. Lyakhov, E. L. Shishkina, Doklady Akademii Nauk, 412:2 (2007), 162–166
Sitnik S.M., Shishkina E.L., “On fractional powers of Bessel operators on half-axes”, Siberian Electronic Mathematical Reports, 2018, № 15, 1–10
Shishkina E.L., Sitnik S.M., “General form of the Euler–Poisson–Darboux equation and application of the transmutation method”, Electronic Journal of Differential Equations, 2017, № 177, 1–20
E. L. Shishkina, A. Khitam, A. M. Qudosi, S. M. Sitnik, “Applications of transmutations of vekua – erd´elyi - lowndes type to differential equations”, Applied Mathematics & Physics, 56:1 (2024), 27–34
2.
A. Ya. Belov, V. M. Buchstaber, V. B. Vasilyev, Yu. P. Virchenko, S. K. Kuizheva, A. G. Kusraev, D. K. Mamyi, A. B. Muravnik, A. V. Pskhu, S. A. Rozanova, Z. A. Saidov, A. L. Semenov, S. M. Sitnik, A. L. Skubachevskii, A. P. Soldatov, E. L. Shishkina, A. G. Yagola, “Sultan Nazhmudinovich Askhabov (on the 70-th anniversary of his birth)”, Chebyshevskii Sb., 25:2 (2024), 5–19
2023
3.
A. L. Dzhabrailov, E. L. Shishkina, “On the generalized Bessel potential and perfect functional completion”, Vestn. St. Petersbg. Univ., Math., 10:2 (2023), 200–211
4.
A. V. Dzarakhohov, E. L. Shishkina, “The problem for a mixed equation with fractional power of the Bessel operator”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 42:1 (2023), 37–57
2022
5.
A. V. Dzarakhohov, E. L. Shishkina, “Solution to the fractional order Euler–Poisson–Darboux equation”, Vladikavkaz. Mat. Zh., 24:2 (2022), 85–100
6.
A. L. Dzhabrailov, E. L. Shishkina, “On the theory of spaces of generalized Bessel potentials”, Vladikavkaz. Mat. Zh., 24:3 (2022), 62–77
7.
A. L. Dzhabrailov, E. L. Shishkina, “Connection between generalized bessel potentials and solutions to the singular heat equation”, Applied Mathematics & Physics, 54:2 (2022), 89–97
2021
8.
D. K. Durdiev, E. L. Shishkina, S. M. Sitnik, “Fractional powers of Bessel operator and its numerical calculation”, Chelyab. fiz.-matem. zhurn., 6:2 (2021), 172–189;
9.
E. L. Shishkina, S. M. Sitnik, I. Jebabli, “Application of integral transforms composition method (ITCM) to obtaining transmutations via integral transforms with Bessel functions in kernels”, Sib. elektron. matem. izv., 18:2 (2021), 884–900;
S. M. Sitnik, E. L. Shishkina, “On two classes of operators of generalized fractional integro-differentiation”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 198, VINITI, Moscow, 2021, 109–122
11.
Kh. Alzamili, E. L. Shishkina, “Weighted homogeneous distribution and its applications”, Applied Mathematics & Physics, 53:4 (2021), 301–311
12.
S. M. Sitnik, E. L. Shishkina, “Review of the monograph: V. V. Kravchenko direct and inverse Sturm - Liouville problems. springer, 2020, in english. language. (with a brief outline of the development of the theory of inverse problems for the Sturm - Liouville equation)”, Applied Mathematics & Physics, 53:1 (2021), 73–84
13.
E. L. Shishkina, “General formula of inversion of weighted spherical mean”, Applied Mathematics & Physics, 53:1 (2021), 13–30
2019
14.
E. L. Shishkina, “General Euler–Poisson–Darboux equation and hyperbolic $B$-potentials”, Partial differential equations, CMFD, 65, no. 2, PFUR, M., 2019, 157–338
15.
E. L. Shishkina, S. M. Sitnik, “A Fractional Equation with Left-Sided Fractional Bessel Derivatives of Gerasimov–Caputo Type”, Mathematics, 7:12, 1216 (2019), 1-21
E. L. Shishkina, “Generalized divergent theorem and second Green identity of $B-$elliptic and $B-$hyperbolic operators”, Applied Mathematics & Physics, 51:4 (2019), 506–513
A. V. Kuznetsov, E. L. Shishkina, S. M. Sitnik, “Probabilistic Properties of Near-Optimal Trajectories of an Agent Moving Over a Lattice”, Journal of Optimization Theory and Applications, 2018, 1-17 (Published online) https://link.springer.com/article/10.1007
A. Fitouhi, I. Jebabli, E. L. Shishkina, S. M. Sitnik, “Applications of the integral transforms composition method to wave-type singular differential equations and index shift transmutations”, Electronic Journal of Differential Equations, 2018:130 (2018), 1-27https://ejde.math.txstate.edu/Volumes/2018/130/abstr.html, arXiv: https://arxiv.org/abs/1805.06925
25.
V. V. Kravchenko, E. L. Shishkina, S. M. Torba, “On a Series Representation for Integral Kernels of Transmutation Operators for Perturbed Bessel Equations”, Math. Notes, 104:4 (2018), 530–544
26.
E. L. Shishkina, “Solution of the singular Cauchy problem for a general inhomogeneous Euler–Poisson–Darboux equation”, Carpathian Journal of Mathematics, 34:2 (2018) , 255- 267 pp.
I. P. Polovinkin, E. L. Shishkina, S. M. Sitnik, “Space of images of the mixed Riesz hyperbolic B-potential and analytic continuation”, Journal of Inverse and Ill-posed Problems, 2018, 10.1515/jiip-2017-0112 (Published online) , 23 pp.
E. L. Shishkina, S. Abbas, “Method of Riesz potentials applied to solution to nonhomogeneous singular wave equations”, Matematicheskie zametki SVFU, 25:3 (2018), 68–91;
D. S. Donchev, S. M. Sitnik, E. L. Shishkina, “On refinements of neo-classical inequality and its applications to stochastic differential equations and Brownian motion”, Chelyab. Fiz.-Mat. Zh., 2:3 (2017), 257–265
30.
E. L. Shishkina, “Inversion of the mixed Riesz hyperbolic B-potentials”, International Journal of Applied Mathematics, 30:6 (2017), 487-500http://diogenes.bg/ijam/contents/2017-30-6/3/
E. L. Shishkina, “Vesovye obobschënnye funktsii, otvechayuschie kvadratichnoi forme s kompleksnymi koeffitsientami”, Chelyabinskii fiziko-matematicheskii zhurnal, 2:1 (2017), 88-98http://cpmj.csu.ru/index.php/cpmj/article/view/66
S. M. Sitnik, E. L. Shishkina, “Drobnye stepeni operatora Besselya na poluosi i ikh svoistva”, Nekotorye aktualnye problemy sovremennoi matematiki i matematicheskogo obrazovaniya Materialy nauchnoi konferentsii, Rossiiskii gosudarstvennyi pedagogicheskii universitet im. A.I. Gertsena, Sankt-Peterburg, 2017, 144-150
S. M. Sitnik, E. L. Shishkina, “On an identity for the iterated weighted spherical mean and its applications 13 (2016), 849–860”, Sib. Èlektron. Mat. Izv., 13 (2016), 849–860
E. L. Shishkina, “Integralnoe predstavlenie yadra operatora, approksimiruyuschego obratnyi operator dlya giperbolicheskogo V-potentsiala Rissa”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 21:2 (2016), 450-458http://journals.tsutmb.ru/go/1810-0198/2016/2/450-458/
43.
O. P. Barabash, E. L. Shishkina, “Reshenie obschego uravneniya Eilera–Puassona–Darbu, soderzhaschee operator Besselya po vsem peremennym”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki., 21:6 (2016), 2146-2151http://journals.tsutmb.ru/go/1810-0198/2016/6/2146-2151/
44.
E. L. Shishkina, “On weighted generalized functions associated with quadratic forms”, Probl. Anal. Issues Anal., 5(23):2 (2016), 52–68
L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina, “Formulas for the solution of the Cauchy problem for a singular wave equation with Bessel time operator”, Doklady Mathematics, 90:3 (2014), 737-742https://link.springer.com/article/10.1134
E. L. Shishkina, “Equality for iterated weighted spherical means generated by generalized translation”, Some current problems in modern mathematics and education in mathematics (St. Petersburg), Izdat. RGPU im. A. I. Gertsena, 2013, 143-145
L. N. Lyakhov, E. L. Shishkina, “Inversion of general Riesz B-potentials with homogeneous characteristic in weight classes of functions”, Doklady Mathematics, 79:3 (2009), 377–381https://link.springer.com/article/10.1134
2007
51.
L. N. Lyakhov, E. L. Shishkina, “General B-hypersingular integrals with homogeneous characteristic”, Doklady Mathematics, 75:1 (2007), 39-43https://link.springer.com/article/10.1134
About singular Klein–Gordon equality E. L. Shishkina, Kh. Alzamili III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 7, 2023 15:35
Обращение гиперболических В-потенциалов Рисса E. L. Shishkina Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics February 14, 2018 16:00
2024
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