quasilinear equations,
convergence of solutions,
homogenization,
localization of support,
perforated domains,
deformation quantization,
invariant connection.
UDC:
517.95, 517.956.25
Subject:
convergence and localization of the support of solutions of semilinear elliptic equations;
invariant linear connections.
Main publications:
S.V.Pikulin, “The Thomas — Fermi Problem and Solutions of the Emden — Fowler Equation”, Computational Mathematics and Mathematical Physics, 59:8 (2019), 1292–1313Springer
S.V.Pikulin, “Traveling-Wave Solutions of the Kolmogorov–Petrovskii–Piskunov Equation”, Computational Mathematics and Mathematical Physics, 58:2 (2018), 230–237
S. V. Pikulin, “Convergence of a family of solutions to a Fujita-type equation in domains with cavities”, Comput. Math. Math. Phys., 56:11 (2016), 1872–1900; Comput. Math. Math. Phys., 56:11 (2016), 1872–1900
S. V. Pikulin, E. A. Tevelev, “Invariant linear connections on homogeneous symplectic varieties”, Transformation Groups, 6:2 (2001), 193–198connections.pdf, arXiv: math/9912091
S. V. Pikulin, “Integral convergence of solutions of the Dirichlet problem for a quasilinear elliptic equation in perforated domains”, Mat. Zametki (to appear)
2024
2.
Bezrodnykh S.I., Pikulin S.V., “Numerical-Analytical Method for Nonlinear Equations
of Kolmogorov–Petrovskii–Piskunov Type”, Computational Mathematics and Mathematical Physics, 2024, 2484–2509
3.
S.I.Bezrodnykh, S.V. Pikulin, “Chislenno-analiticheskii metod dlya kvazilineinykh
uravnenii tipa Kolmogorova — Petrovskogo —
Piskunova s singulyarnym vozmuscheniem”, Sbornik materialov mezhdunarodnoi konferentsii KROMSh-2024, XXXV Krymskaya Osennyaya
Matematicheskaya Shkola-simpozium
N.D. Kopachevskogo po spektralnym
i evolyutsionnym zadacham (Kacha (Sevastopol), RF, 7-16 sentyabrya 2024 g.), ISBN 978-5-907742-61-1, IT «ARIAL», Simferopol, 2024, 96–98Sbornik tezisov
4.
Bezrodnykh S.I., Pikulin S.V., “Numerical-analytical method for the Burgers equation with a periodic boundary condition”, Journal of Mathematical Sciences, 285 (2024), 301–315
2023
5.
S.I.Bezrodnykh, S.V.Pikulin, “O chislenno-analiticheskom metode dlya uravneniya Byurgersa”, 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. Abstracts. (5–13 iyulya 2023 g., g. Dolgoprudnyi), ISBN: 978-5-6048945-7-6, MPDSIDA-2023, Dolgoprudnyi, 2023, 224-225MathNet
6.
S. V. Pikulin, “On the Estimate of Integral Norm of Solution of the Dirichlet Problem for Quasilinear Elliptic Equation”, Math. Notes, 114:4 (2023), 639–642
S.V. Pikulin, “On Analytic Continuation of Conformal Mapping of a Circular Triangle”, Computational Mathematics and Mathematical Physics, 62:12 (2022), 2112–2122Springer
9.
S.V.Pikulin, “Analitiko-chislennyi metod dlya uravneniya Byurgersa s periodicheskim kraevym usloviem”, Sbornik materialov mezhdunarodnoi konferentsii KROMSh-2022, XXXIII Krymskaya Osennyaya Matematicheskaya Shkola-simpozium po spektralnym i evolyutsionnym zadacham (Satera (Alushta), Respublika Krym, Rossiiskaya Federatsiya, 16 – 25 sentyabrya 2022 g.), ISBN 978-5-907587-87-8, eds. Muratov M.A., Skubachevskii A.L., Suslina T.A., Shkalikov A.A., Zakora D.A., Pashkova Yu.S., Starkov P.A., Forduk K.V., Yakubova A.R., IT «ARIAL», Simferopol, 2022, 52Sait konferentsii
2021
10.
S.V.Pikulin, “O metode resheniya nachalno–kraevoi zadachi dlya nelineinogo parabolicheskogo uravneniya”, Sbornik materialov mezhdunarodnoi konferentsii KROMSh-2021, XXXII Krymskaya Osennyaya Matematicheskaya Shkola-simpozium
po spektralnym i evolyutsionnym zadacham (Krym, Satera, 17-26 sentyabrya 2021 goda), ISBN 978-5-6046943-4-3, Poliprint, Simferopol, 2021, 103Materialy
2020
11.
S.V.Pikulin, “Parametrization of Solutions to the Emden–Fowler Equation
and the Thomas–Fermi Model of Compressed Atoms”, Computational Mathematics and Mathematical Physics, 60:8 (2020), 1271–1283Springer
12.
S.V.Pikulin, “Zadacha Dirikhle dlya kvazilineinogo uravneniya s dvoinoi nelineinostyu i effekt lokalizatsii vozmuscheniya”, Sbornik materialov mezhdunarodnoi konferentsii KROMSh-2020. XXXI Krymskaya Osennyaya Matematicheskaya Shkola-simpozium po spektralnym i evolyutsionnym zadacham, ISBN 978-5-6045196-1-5 (Krym, Laspi, 19-26 sentyabrya 2020 g.), Poliprint, Simferopol, 2020, 179–181Materialy
2019
13.
S.V.Pikulin, “Skhodimost reshenii kvazilineinogo ellipticheskogo uravneniya v oblasti s sharovoi polostyu”, Sovremennye problemy matematiki i mekhaniki. Materialy mezhdunarodnoi konferentsii, posvyaschennoi 80–letiyu akademika RAN V.A.Sadovnichego., ISBN 978-5-317-06134-0 (Moskva, 13–15 maya 2019 g.), Tom 1, MAKS Press, Moskva, 2019, 336–338Na saite konferentsii
S.V.Pikulin, “The Thomas — Fermi Problem and Solutions of the Emden — Fowler Equation”, Computational Mathematics and Mathematical Physics, 59:8 (2019), 1292–1313Springer
16.
S.V.Pikulin, “Analitiko–chislennyi metod resheniya zadachi Tomasa — Fermi”, The First International Conference “Mathematical Physics, Dynamical Systems, Infinite Dimensional Analysis” MPhDSIDA-2019. Book of Abstracts (Dolgoprudnyi, 17-21 iyunya 2019 g.), MFTI, 2019, 145
17.
S.V.Pikulin, “Analitiko–chislennyi metod resheniya uravneniya Emdena — Faulera i model Tomasa — Fermi”, Sbornik materialov mezhdunarodnoi konferentsii KROMSh-2019.
XXX Krymskaya Osennyaya Matematicheskaya Shkola–simpozium po spektralnym i evolyutsionnym zadacham, ISBN 978-5-6043331-6-7 (Laspi, Krym, 17–29 sentyabrya 2019 g.), Poliprint, Simferopol, 2019, 120–123Materialy konferentsii
18.
S.V.Pikulin, “Analytical-Numerical Method for
Calculating the Thomas–Fermi Potential”, Russian Journal of Mathematical Physics, 26:4 (2019), 544–552Springer
S.V.Pikulin, “Traveling-Wave Solutions of the Kolmogorov–Petrovskii–Piskunov Equation”, Computational Mathematics and Mathematical Physics, 58:2 (2018), 230–237Springer
20.
S.V.Pikulin, “The Behavior of Solutions to a Special Abel Equation of the Second Kind near a Nodal Singular Point”, Computational Mathematics and Mathematical Physics, 58:12 (2018), 1948–1966Springer
S.V.Pikulin, “Ob analitiko-chislennom metode resheniya uravneniya Abelya II roda s prilozheniem k modeli raspredeleniya vnutriatomnogo potentsiala”, Sobolevskie chteniya, Tezisy dokladov (Novosibirsk, Rossiya, 10-16 dekabrya 2018 g.), eds. G.V.Demidenko, izd-vo Instituta matematiki SO RAN, Novosibirsk, 2018, 142
2017
24.
S.V.Pikulin, “O promezhutochnykh asimptoticheskikh rezhimakh v nekotorykh modelyakh teorii goreniya”, Tavricheskii vestnik informatiki i matematiki, 2017, no. 3 (36), 55–72TVIM 2017 #3
2016
25.
S.V.Pikulin, “Convergence of a Family of Solutions to a Fujita-Type Equation in Domains with Cavities”, Computational Mathematics and Mathematical Physics, 56:11 (2016), 1872–1900Springer
26.
S. V. Pikulin, “Ob analiticheskom metode vychisleniya potentsiala vnutri tyazhelogo iona v modeli Tomasa"– Fermi”, Aktualnye problemy prikladnoi matematiki i mekhaniki. Tezisy dokladov VIII Vserossiiskoi konferentsii, posvyaschennoi pamyati akademika A. F. Sidorova i Vserossiiskoi molodezhnoi shkoly–konferentsii. (5–10 sentyabrya 2016 g.), eds. M. Yu. Filimonov, IMM UrO RAN, Ekaterinburg, 2016, 84–85
27.
S. V. Pikulin, “Ob effektivnom analitiko–chislennom metode resheniya uravneniya Kolmogorova−Petrovskogo−Piskunova v kvazistatsionarnom sluchae”, XXI Vserossiiskaya konferentsiya “Teoreticheskie osnovy i konstruirovanie chislennykh algoritmov dlya resheniya zadach matematicheskoi fiziki”, posvyaschennoi pamyati K.I.Babenko. Tezisy dokladov. (Novorossiisk, Abrau–Dyurso, 5–11 sentyabrya 2016 g.), ISBN: 978-5-98354-024-8, eds. A. L. Afendikov, IPM im. M. V. Keldysha, 2016, 103–104Sbornik na saite konferentsii
28.
S.V.Pikulin, “O skhodimosti reshenii zadachi Dirikhle dlya kvazilineinogo ellipticheskogo uravneniya v oblastyakh s sharovymi polostyami”, XXVII Krymskaya osennyaya matematicheskaya Shkola–simpozium po spektralnym i evolyutsionnym zadacham (KROMSh-2016): sbornik tezisov. (Batiliman (Laspi), RF, 17–29 sentyabrya 2016), eds. N.D.Kopachevskii, OOO Forma, Simferopol, 2016, 55–56
2015
29.
S. V. Pikulin, “Ob odnom svoistve reshenii uravneniya, modeliruyuschego nekotorye khimicheskie reaktsii”, Matematicheskoe modelirovanie, 27:7 (2015), 97–102
S. V. Pikulin, “Ob odnom svoistve reshenii uravneniya, modeliruyuschego nekotorye khimicheskie reaktsii”, «Sovremennye problemy prikladnoi matematiki i informatiki». Mezhdunarodnaya molodëzhnaya konferentsiya. Tezisy dokladov. (Dubna, 25 – 29 avgusta 2014 g.), OIYaI, Dubna, 2014, 107–108
33.
S. V. Pikulin, “O raspolozhenii "mertvoi zony" resheniya zadachi Dirikhle dlya uravneniya tipa Fudzhity”, Mezhdunarodnaya konferentsiya "KROMSh–2014. Krymskaya Osennyaya Matematicheskaya Shkola-simpozium po spektralnym i evolyutsionnym zadacham.". Sbornik tezisov. (Sudak, Rossiiskaya Federatsiya, 21 sentyabrya – 30 sentyabrya 2014 goda), TNU im. V. I. Vernadskogo, 2014, 53–54
2013
34.
D. V. Zakablukov, S. V. Pikulin, A. A. Chilikov, “Raspredelennaya sistema vosstanovleniya parolei”, Cluster Computing, Second International Conference CC2013.Collection of scientific papers. (Lvov, 3–5 iyunya 2013 g.), eds. V. Cherepynets, Lviv Polytechnic National Institute, Lviv, 2013, 248–251http://hpc-ua.org/cc-13/files/proceedings/55.pdf
Pikulin S. V., “O skhodimosti reshenii polulineinykh ellipticheskikh uravnenii v semeistve perforirovannykh oblastei”, Mezhdunarodnaya nauchnaya konferentsiya «Sovremennye metody i problemy teorii operatorov i garmonicheskogo analiza i ikh prilozheniya III». Tezisy dokladov. (Rostov-na-Donu, 2–6 iyunya 2013 g.), YuFU, 2013, 73
37.
S. V. Pikulin, “O printsipe kompaktnosti nositelya resheniya dlya polulineinykh ellipticheskikh uravnenii”, Differentsialnye uravneniya. Funktsionalnye prostranstva. Teoriya priblizhenii. Mezhdunarodnaya konferentsiya, posvyaschennaya 105-letiyu so dnya rozhdeniya S. L. Soboleva. Tezisy dokladov. (Novosibirsk, 18–24 avgusta 2013 g.), Institut matematiki im. S.L.Soboleva SO RAN, 2013, 217
38.
S. V. Pikulin, “O skhodimosti reshenii ellipticheskikh uravnenii so slaboi nelineinostyu”, Krymskaya Mezhdunarodnaya Matematicheskaya Konferentsiya. Sbornik tezisov. Tom 2. (Sudak, Ukraina, 22 sentyabrya – 4 oktyabrya 2013 goda), TNU im. V. I. Vernadskogo, 2013, 53
S. V. Pikulin, “O skhodimosti reshenii statsionarnogo uravneniya tipa Fudzhity v oblasti s sharovoi polostyu”, Nauchnye Vedomosti Belgorodskogo gosudarstvennogo universiteta. Matematika. Fizika., 2013, no. 19 (162), vyp. 32, 120–129 "Nomer zhurnala"
2012
41.
S. V. Pikulin, “Behavior of solutions of semilinear elliptic equations in domains with complicated boundary”, Russian Journal of Mathematical Physics, 19:3 (2012), 401–404Springer
S. V. Pikulin, Osrednenie i lokalizatsiya reshenii nekotorykh kraevykh zadach dlya polulineinykh el-lipticheskikh uravnenii v perforirovannykh oblastyakh, Diss. … kand. fiz.-matem. nauk, mekhaniko-matematicheskii fakultet MGU im. M. V. Lomonosova, Moskva, 2012 , 99 pp.
43.
S. V. Pikulin, “Lokalizatsiya nositelya i usrednenie reshenii polulineinykh ellipticheskikh uravnenii v perforirovannykh oblastyakh”, «Matematicheskaya fizika i ee prilozheniya», Tretya mezhdunarodnaya konferentsiya. Materialy konferentsii. (Samara, 27 avgusta – 1 sentyabrya 2012 g.), SamGTU, Samara, 2012, 232–233
44.
S. V. Pikulin, “Osrednenie reshenii nekotorykh kvazilineinykh ellipticheskikh uravnenii i effekt «mertvoi zony»”, «Sovremennye problemy prikladnoi matematiki i informatiki», Mezhdunarodnaya molodezhnaya konferentsiya — shkola. Tezisy dokladov. (Dubna, 22 – 27 avgusta 2012 g.), OIYaI, Dubna, 2012, 161–163
2002
45.
H. Matevossian, S. V. Pikulin, “On the homogenization of semilinear elliptic operators in perforated domains”, Sb. Math., 193:3 (2002), 409–422
2001
46.
S. V. Pikulin, E. A. Tevelev, “Invariant linear connections on homogeneous symplectic varieties”, Transformation Groups, 6:2 (2001), 193–198connections.pdf, arXiv: math/9912091
H. Matevossian, S. V. Pikouline, “On the homogenization of weakly nonlinear divergent operators in a perforated cube”, Math. Notes, 68:3 (2000), 337–344
48.
O. A. Matevosyan, S. V. Pikulin, Usrednenie reshenii ellipticheskikh operatorov s nelineinym pogloscheniem v perforirovannykh oblastyakh, Preprint MGU im. M. V. Lomonosova, MAKS Press, Moskva, 2000 , 27 pp.
1999
49.
O. A. Matevosyan, S. V. Pikulin, “The homogenization of solutions of elliptic differential operators with weak nonlinearity in perforated domains”, Proceedings of the Mathematische Arbeitstagung on the «Fourth Arbeitstagung of the Second Series» (Bonn, June 18−24, 1999), Max-Planck-Institut fur Mathematik, Bonn, 1999, 425
Presentations in Math-Net.Ru
1.
On the numerical-analytical method for the Burgers equation S. V. Pikulin, S. I. Bezrodnykh 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 5, 2023 15:05
2024
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