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, “General Euler–Poisson–Darboux equation and hyperbolic $B$-potentials”, Partial differential equations, CMFD, 65, no. 2, PFUR, M., 2019, 157–338
2.
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 (cited: 1)
3.
E. L. Shishkina, “The Dirichlet problem for an elliptic singular equation”, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2019, 1-10 (cited: 1)
4.
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
2018
5.
E. L. Shishkina, “Properties of Mixed Hyperbolic B–Potential”, Progress in Fractional Differentiation and Applications, 4:2 (2018), 83-98 http://www.naturalspublishing.com/Article.asp?ArtcID=13666 (cited: 3)
6.
E. L. Shishkina, “Singular Cauchy problem for the general Euler-Poisson-Darboux equation”, Open Mathematics, 16:1 (2018), 23–31 (Published online) https://www.degruyter.com/view/j/math.2018.16.issue-1/math-2018-0005/math-2018-0005.xml (cited: 4) (cited: 5)
7.
E. L. Shishkina, “Generalized Euler-Poisson-Darboux equation and singular Klein–Gordon equation”, Journal of Physics: Conference Series, 973:1 (2018), 1-20 http://iopscience.iop.org/article/10.1088/1742-6596/973/1/012058/pdf (cited: 4)
8.
S. M. Sitnik, E. L. Shishkina, “On fractional powers of the Bessel operator on semiaxis”, Sib. Èlektron. Mat. Izv., 15:1 (2018), 1-10 http://semr.math.nsc.ru/v15/p1-10.pdf, arXiv: https://arxiv.org/pdf/1706.01928.pdf
9.
E. L. Shishkina, M. Karabacak, “Singular Cauchy problem for generalized homogeneous Euler-Poisson-Darboux equation”, Matematicheskie zametki SVFU, 25:2 (2018), 85-96 https://www.s-vfu.ru/universitet/rukovodstvo-i-struktura/instituty/niim/mzsvfu/issues/2018-2/85-96.pdf
10.
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 (cited: 1)
11.
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), 1-27 https://ejde.math.txstate.edu/Volumes/2018/130/abstr.html, arXiv: https://arxiv.org/abs/1805.06925 (cited: 1) (cited: 8)
12.
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 (cited: 3) (cited: 5)
13.
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.
14.
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.
2017
15.
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
16.
E. L. Shishkina, “Inversion of the mixed Riesz hyperbolic B-potentials”, International Journal of Applied Mathematics, 30:6 (2017), 487-500 http://diogenes.bg/ijam/contents/2017-30-6/3/ (cited: 5)
17.
E. L. Shishkina, S. M. Sitnik, “General form of the Euler-Poisson-Darboux equation and application of the transmutation method”, Electron. J. Differential Equations, 2017, 177, 1-20 https://ejde.math.txstate.edu/Volumes/2017/177/shishkina.pdf, arXiv: arXiv:1707.04733 (cited: 1) (cited: 14)
18.
E. L. Shishkina, S. M. Sitnik, “On fractional powers of Bessel operators”, Journal of Inequalities and Special Functions, 8:1 (2017), 49-67 http://www.ilirias.com/jiasf/repository/docs/JIASF8-1-5.pdf, arXiv: arXiv:1703.02232 (cited: 10)
19.
E. L. Shishkina, “Vesovye obobschënnye funktsii, otvechayuschie kvadratichnoi forme s kompleksnymi koeffitsientami”, Chelyabinskii fiziko-matematicheskii zhurnal, 2:1 (2017), 88-98 http://cpmj.csu.ru/index.php/cpmj/article/view/66 (cited: 3)
20.
D. S. Donchev, S. M. Sitnik., E. L. Shishkina, “Ob obobschenii binominalnoi teoremy, voznikayuschem v teorii differentsialnykh uravnenii”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika., 49:27 (276) (2017), 19-25 https://cyberleninka.ru/article/n/ob-obobschenii-binominalnoy-teoremy-voznikayuschem-v-teorii-differentsialnyh-uravneniy
21.
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
2016
22.
L. N. Lyakhov, E. L. Shishkina, “Weighted mixed spherical means and singular ultrahyperbolic equation”, Analysis: International mathematical journal of analysis and its applications, 36:2 (2016), 65-70 https://www.degruyter.com/view/j/anly.2016.36.issue-2/anly-2015-5006/anly-2015-5006.xml (cited: 2)
23.
E. L. Shishkina, “On weighted generalized functions associated with quadratic forms”, Probl. Anal. Issues Anal., 5 (23):2 (2016), 52-68 http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3390, arXiv: 1612.07907 (cited: 2) (cited: 1) (cited: 2)
24.
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
25.
E. L. Shishkina, “On the boundedness of hyperbolic Riesz B-potential”, Lithuanian Mathematical Journal, 56:4 (2016), 540–551 https://link.springer.com/article/10.1007/s10986-016-9335-y (cited: 5) (cited: 8)
26.
L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina, “Accompanying Distributions of Singular Differential Operators”, Journal of Mathematical Sciences, 219:2 (2016), 184–189 https://link.springer.com/article/10.1007/s10958-016-3095-4 (cited: 1)
27.
E. L. Shishkina, “O svoistvakh odnogo usrednyayuschego yadra v vesovom klasse Lebega”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika., 42:6 (227) (2016), 12-19 https://cyberleninka.ru/article/n/o-svoystvah-odnogo-usrednyayuschego-yadra-v-vesovom-klasse-lebega
28.
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), 450-458 http://journals.tsutmb.ru/go/1810-0198/2016/2/450-458/
29.
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), 2146-2151 http://journals.tsutmb.ru/go/1810-0198/2016/6/2146-2151/
30.
E. L. Shishkina, “On weighted generalized functions associated with quadratic forms”, Probl. Anal. Issues Anal., 5(23):2 (2016), 52–68 (cited: 2) (cited: 1) (cited: 2)
2014
31.
L. N. Lyakhov, I. P. Polovinkin, E. L. Shishkina, “On a Kipriyanov problem for a singular ultrahyperbolic equation”, Differential Equations, 50:4 (2014), 513-525 https://link.springer.com/article/10.1134/S0012266114040090 (cited: 10) (cited: 17)
32.
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), 737-742 https://link.springer.com/article/10.1134 (cited: 8) (cited: 11)
2013
33.
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
2009
34.
E. L. Shishkina, “Inversion of integral of B-potential type with density from Φγ”, Journal of Mathematical Sciences, 160:1 (2009), 95-102 https://link.springer.com/article/10.1007/s10958-009-9487-y (cited: 5)
35.
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), 377–381 https://link.springer.com/article/10.1134 (cited: 1) (cited: 1)
2007
36.
L. N. Lyakhov, E. L. Shishkina, “General B-hypersingular integrals with homogeneous characteristic”, Doklady Mathematics, 75:1 (2007), 39-43 https://link.springer.com/article/10.1134 (cited: 1) (cited: 5)
2006
37.
L. N. Lyakhov, E. L. Shishkina, “Generalized Riesz B-potentials of the mixed type”, Doklady Mathematics, 73:1 (2006), 42-45 (cited: 4) (cited: 7)
38.
E. L. Shishkina, “Obobschennaya vesovaya funktsiya r^\lambda”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2006, no. 1, 215-221 http://www.vestnik.vsu.ru/pdf/physmath/2006/01/shishkina_rus.pdf
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
2019
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