01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
Keywords:
symmetries,
Lie algebras,
integrability,
parabolic equation,
the Navier–Stokes equations,
stabilization of solutions.
Subject:
The criterion of uniform stabilization of solutions to the first mixed problem for a parabolic equation in unbounded domain was established. The decay rate of solutions to the Navier–Stokes equations in unbounded three dimensional domain was established. Jointly with A. A. Bormisov and E. S. Gudkova it was shown that for every hiperbolic system of Riccati type is corresponded by natural way a $Z$-graded Lie algebra. This result permited (jointly with A. A. Bormisov) to describe the symmetries of hiperbolic system of Riccati type corresponded to the affine Kac-Moody algebras.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1977 (department of differential equations). Ph. D. thesis was defended in 1981. D. Sci. thesis was defended in 1994. A list of my works contains more than 100 titles. Since 1978 I and K. B. Sabitov have led the research seminar at MSU on differential equations.
V. F. Vil'danova, F. Kh. Mukminov, “Entropy solution for an equation with measure-valued potential in a hyperbolic space”, Sb. Math., 214:11 (2023), 1534–1559
2.
N. A. Vorobev, F. Kh. Mukminov, “Existence of a Renormalized Solution of a Parabolic Problem in Anisotropic Sobolev–Orlicz Spaces”, Journal of Mathematical Sciences, 258:3 (2021), 37–64
V. F. Vil’danova and F. Kh. Mukminov, “Perturbations of Nonlinear Elliptic Operators by Potentials in the Space of Multiplicators”, Journal of Mathematical Sciences, 257:5 (2021), 569–578
V. F. Vil’danova and F. Kh. Mukminov, “Existence of Weak Solutions of the Aggregation Equation with the p(·)-Laplacian”, Journal of Mathematical Sciences, 252:2 (2021), 156-167
5.
V. F. Vilfanova, F. Kh. Mukminov, “Existence of Weak Solutions of Aggregation Integro-Differential Equations”, Journal of Mathematical Sciences, 259:6 (2021), 775-790
6.
F. Kh. Mukminov, “Existence and Uniqueness of Renormalized Solutions to Parabolic Problems for Equations with Diffuse Measure”, Journal of Mathematical Sciences, 247:6 (2020), 900-925
7.
F. Kh. Mukminov, “Existence of a Renormalized Solution to an Anisotropic Parabolic Problem for an Equation with Diffuse Measure”, Proc. Steklov Inst. Math., 306 (2019), 178–195
8.
N. A. Vorobyev, F. Kh. Mukminov, “Existence of a renormalized solution of a parabolic problem in anisotropic Sobolev–Orlicz spaces”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 39–64
9.
F. Kh. Mukminov, “Existence of a renormalized solution to an anisotropic parabolic problem with variable nonlinearity exponents”, Sb. Math., 209:5 (2018), 714–738
10.
T. R. Gadyl'shin, F. Kh. Mukminov, “Perturbation of second order nonlinear equation by delta-like potential”, Ufa Math. Journal, 10:2 (2018), 31–43
11.
V. F. Vil'danova, F. Kh. Mukminov, “Existence of Weak Solutions of Aggregation Equation with the $p(\cdot)$-Laplacian”, J. Math. Sci. (N. Y.), 252:2 (2021), 156–167
12.
I. I. Kiryanov, F. H. Mukminov, A. R. Tulyabaev, L. M. Khalilov, “Neural network for prediction of C-13 NMR chemical shifts of fullerene C-60 mono-adducts”, JOURNAL OF CHEMOMETRICS, 32:9 (2018), e3037https://onlinelibrary.wiley.com/doi/full/10.1002/cem.3037
F .Kh. Mukminov, “Suschestvovanie renormalizovannogo resheniya anizotropnoi parabolicheskoi zadachi dlya uravneniya s diffuznoi meroi”, Spektralnaya teoriya i smezhnye voprosy. Sbornik tezisov. (Ufa, 1-4 oktyabrya 2018 goda), eds. R. N. Garifullin, IPK BGPU, Ufa, 2018, c.119http://matem.anrb.ru/conf/sbor_oct.pdf
14.
F. Kh. Mukminov, “Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces”, Sb. Math., 208:8 (2017), 1187–1206
15.
F. Kh. Mukminov, È. R. Andriyanova, “Existence of weak solutions to an elliptic-parabolic equation with variable order of nonlinearity”, Journal of Mathematical Sciences, 241:3 (2019), 290–305
16.
F. Kh.Mukminov, V. F. Vildanova, “The existence of a unique weak solution to the problem for the aggregation equation with the p()-Laplacian”, The 8th International Conference on Differerential and Functional Equations (Moscow, Russia, August 13-20, 2017), Tipografiya RUDN, Moskva, 2017, 186
17.
V. F. Vildanova, F. Kh. Mukminov, “Suschestvovanie slabogo resheniya integro-differentsialnogo uravneniya agregatsii”, Sovremennaya matematika. Fundamentalnye napravleniya., 64:4 (2017), 557–572
I. I. Kiryanov, F. H. Mukminov, A. R. Tulyabaev, L. M. Khalilov, “Prediction of^{13} C NMR chemical shifts by artificial neural network. I. Partial charge model as atomic descriptor”, Chemometrics and Intelligent Laboratory Systems, 152 (2016), 62–68https://www.researchgate.net/publication/291554638
È. R. Andriyanova, F. Kh. Mukminov, “Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity”, Sb. Math., 207:1 (2016), 1–40
20.
F. Kh. Mukminov, “Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation”, Ufa Math. Journal, 8:2 (2016), 44–57
21.
F. Kh. Mukminov, T. R. Gadylshin, “Boundary-value problem for a second-order nonlinear equation with delta-like potential”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 216–230
22.
V. F. Vil'danova, F. Kh. Mukminov, “Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds”, Ufa Math. Journal, 7:2 (2015), 55–63
23.
E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. Journal, 6:4 (2014), 31–47
24.
V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597
25.
È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Sb. Math., 204:9 (2013), 1239–1263
26.
L. M. Kozhevnikova, F. Kh. Mukminov, “Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains”, Proc. Steklov Inst. Math., 278 (2012), 106–120
27.
V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71
28.
V. F. Gilimshina, F. Kh. Mukminov, “On decay rate of solution to degenerating linear parabolic equations”, Ufimsk. Mat. Zh., 3:4 (2011), 43–56
29.
E. R. Andriyanova, F. Kh. Mukminov, “The lower estimate of decay rate of solutions for doubly nonlinear parabolic equations”, Ufimsk. Mat. Zh., 3:3 (2011), 3–14
30.
F. Kh. Mukminov, E. R. Andriyanova, “Ob otsenke snizu reshenii parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Materialy mezhdunarodnoi konferentsii, posvyaschennoi pamyati A. G. Kostyuchenko. Spektralnaya teoriya operatorov i ee prilozheniya (Ufa, iyun 2011), RITs BashGU, Ufa, 2011, 13
31.
I. M. Bikkulov, F. Kh. Mukminov, “Classes of uniqueness for solutions of the Rickyies problem to fourth and sixth order elliptic equations”, Ufimsk. Mat. Zh., 2:1 (2010), 35–51
32.
A. R. Gerfanov, F. H. Mukminov, “A wide class of uniqueness of the solution for non-uniformly elliptic equation in unbounded domain”, Ufimsk. Mat. Zh., 1:3 (2009), 11–27
33.
F. Kh. Mukminov, A. R. Gerfanov, “Neravenstvo Fridrikhsa dlya odnogo psevdodifferentsialnogo operatora”, Sbornik nauchnykh statei fiziko-matematicheskogo fakulteta BGPU, Uchenye zapiski, vyp.8, Izd-vo BGPU, Ufa, 2007, 18–21
34.
L. M. Kozhevnikova, F. Kh. Mukminov, “Decay of the solution of the first mixed problem for a high-order parabolic equation with minor terms”, J. Math. Sci., 150:5 (2008), 2369–2383
35.
F. Kh. Mukminov, I. M. Bikkulov, “Stabilization of the norm of the solution of a mixed problem in an unbounded domain for parabolic equations of orders 4 and 6”, Sb. Math., 195:3 (2004), 413–440
36.
L. M. Kozhevnikova, F. Kh. Mukminov, “On the Decay of the $\mathbf L_2$-Norm of the Solution of the First Mixed Problem for a Nonlinear System of Parabolic Equations in a Domain with Nonregular Boundary”, Differ. Equ., 38:8 (2002), 1149–1154
37.
A. A. Bormisov, F. Kh. Mukminov, “Symmetries of Systems of the Hyperbolic Riccati Type”, Theoret. and Math. Phys., 127:1 (2001), 446–459
38.
K. B. Sabitov, F. Kh. Mukminov, “The sign of the conormal derivative of a solution to a degenerating elliptic equation near a point of maximum”, Differ. Equ., 36:6 (2000), 938–942
39.
L. M. Kozhevnikova, F. Kh. Mukminov, “Estimates of the stabilization rate as $t\to\infty$ of solutions of the first mixed problem for a quasilinear system of second-order parabolic equations”, Sb. Math., 191:2 (2000), 235–273
40.
F. Kh. Mukminov, “On the set of limit functions for solutions of the nonstationary exterior Stokes problem”, Differ. Equ., 33:8 (1997), 1108–1112
41.
A. A. Bormisov, E. S. Gudkova, F. Kh. Mukminov, “On integrability of Rikkati-type systems of hyperbolic equations”, Theoret. and Math. Phys., 113:2 (1997), 1418–1430
42.
F. Kh. Mukminov, K. B. Sabitov, “O znake kosoi proizvodnoi resheniya vyrozhdayuschikhsya ellipticheskikh uravnenii i ego primeneniya v uravneniyakh smeshannogo tipa”, Mezhdunarodnaya nauchnaya konferentsiya, posvyaschennaya 90-letiyu so dnya rozhdeniya prof. S. P. Pulkina, Tezisy dokladov (Samara, 27-30 maya 1997g.,), SamGPU, Samara, 1997, 54–55
43.
F. Kh. Mukminov, E. S. Gudkova, V. V. Sokolov, “Zadacha Gursa dlya integriruemoi sistemy nelineinykh uravnenii giperbolicheskogo tipa”, Mezhdunarodnaya nauchnaya konferentsiya, posvyaschennaya 90-letiyu so dnya rozhdeniya prof. S. P. Pulkina, Tezisy dokladov (Samara, 27-30 maya 1997g.), SamGPU, Samara, 1997, 23–24
44.
F. Kh. Mukminov, E. S. Gudkova, “Ob integriruemosti po Darbu sistem giperbolicheskikh uravnenii, sootvetstvuyuschikh prostym algebram Li v standartnoi graduirovke”, Trudy vserossiiskoi nauchnoi konferentsii “Fizika kondensirovannogo sostoyaniya”, Tom I. Matematicheskie metody fiziki (Sterlitamak, 1997), Sterlitamakskii GPI, Sterlitamak, 1997, 45–50
45.
N. M. Asadullin, F. Kh. Mukminov, “Uniqueness classes for a non-stationary system of Stokes equations in unbounded domains”, Sb. Math., 187:3 (1996), 315–333
46.
F. Kh. Mukminov, “O zatukhanii ploskogo techeniya vyazkoi neszhimaemoi zhidkosti v neogranichennoi oblasti”, Kompleksnyi analiz, differentsialnye uravneniya, chislennye metody i prilozheniya, Trudy mezhdunarodnoi konferentsii t3, DU (Ufa, 1996), RITs BashGU, Ufa, 1996, 122-130
47.
F. Kh. Mukminov, K. B. Sabitov, “K voprosu o edinstvennosti resheniya zadachi Gellerstedta”, Mezhdunarodnaya konferentsiya, posvyaschennaya 60-letiyu akademika A. M. Nakhusheva, Tezisy dokladov (Nalchik, 3-7 dekabrya 1996 g.), Nalchik, 1996, 75–76
48.
F. Kh. Mukminov, “On uniform stabilization of solutions of the exterior problem for the Navier–Stokes equations”, Russian Acad. Sci. Sb. Math., 81:2 (1995), 297–320
49.
F. Kh. Mukminov, “Of the first mixed problem for the system of Navier–Stokes equations in domains with noncompact boundaries”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 507–524
50.
F. Kh. Mukminov, “Uniform stabilization of the solutions of the exterior problem for Navier–Stokes equations”, Dokl. Math., 48:2 (1994), 248–250
51.
F. Kh. Mukminov, “On the decay of a solution of a mixed problem for a linearized system of Navier–Stokes equations”, Differ. Equ., 28:8 (1992), 1156–1164
52.
F. Kh. Mukminov, “On decay of a solution of the first mixed problem for the linearized system of Navier–Stokes equations in a domain with noncompact boundary”, Russian Acad. Sci. Sb. Math., 77:1 (1994), 245–264
53.
F. Kh. Mukminov, “On the rate of decay of the solution of a mixed problem for a system of Navier–Stokes equations in a domain with a noncompact boundary”, Dokl. Math., 45:3 (1992), 688–691
54.
F. Kh. Mukminov, “On uniform stabilization of solutions of the first mixed problem for a parabolic equation”, Math. USSR-Sb., 71:2 (1992), 331–353
55.
F. Kh. Mukminov, “On straightening the characteristics of a quasilinear second-order equation”, Theoret. and Math. Phys., 75:1 (1988), 340–345
56.
F. Kh. Mukminov, Differ. Uravn., 23:10 (1987), 1772–1780
57.
F. Kh. Mukminov, V. V. Sokolov, “Integrable evolution equations with constraints”, Math. USSR-Sb., 61:2 (1988), 389–410
58.
F. Kh. Mukminov, “Stabilization of solutions of the first mixed problem for a parabolic equation of second order”, Math. USSR-Sb., 39:4 (1981), 449–467
59.
F. Kh. Mukminov, Differ. Uravn., 15:11 (1979), 2021–2033
Proceedings
60.
N. A. Vorobev, F. Kh. Mukminov, “Suschestvovanie renormalizovannogo resheniya parabolicheskoi zadachi v anizotropnykh prostranstvakh Soboleva-Orlicha”, Mezhdunarodnaya matematicheskaya konferentsiya po teorii funktsii, posvyaschennaya 100-letiyu chl.-korr. AN SSSR A.F.Leonteva (Ufa, 24-27 maya, 2017 g.), RITs BashGU, Ufa, 2017, 36-37
61.
F .Kh. Mukminov, E. R .Andriyanova, “Suschestvovanie i edinstvennost renormalizovannogo resheniya parabolicheskogo uravneniya s dvoinoi peremennoi nelineinostyu”, Ufimskaya matematicheskaya konferentsiya s mezhdunarodnym uchastiem, Sbornik tezisov (g.Ufa, 27–30 sentyabrya 2016g.), RITs BashGU, Ufa, 2016, 111–112
62.
F. Kh .Mukminov, “Edinstvennost renormalizovannogo resheniya anizotropnoi parabolicheskoi zadachi s peremennymi nelineinostyami”, Mezhdunarodnaya konferentsiya po differentsialnym uravneniyam i dinamicheskim sistemam, tezisy dokladov (Suzdal 8–12 iyulya 2016 goda), M.:MIAN, Moskva, 2016, 143–144http://agora.guru.ru/diff2016
F. Kh .Mukminov, “Edinstvennost renormalizovannogo resheniya elliptiko-parabolicheskoi zadachi”, Sovremennye metody i problemy teorii operatorov i garmonicheskogo analiza i ikh prilozheniya, Tezisy konferentsii OTHA (Rostov-na-Donu 24–29 aprelya 2016 g.), Izdatelskii tsentr DGTU, Rostov-na-Donu, 2016, 108-109
F. Kh. Mukminov, E. R. Andriyanova, “Parabolicheskoe uravnenie s nestepennymi nelineinostyami: suschestvovanie, edinstvennost i svoistva resheniya”, Spektralnye zadachi, nelineinyi i kompleksnyi analiz, Materialy mezhdunarodnoi nauchnoi konferentsii (Ufa, 24-26 sentyabrya 2014 g.), RITs BashGU, Ufa, 2014, 53–55
67.
F. Kh. Mukminov, E. R. Andriyanova, “Kachestvennye svoistva parabolicheskogo uravneniya s nestepennymi nelineinostyami”, Matematicheskoe modelirovanie protsessov i sistem, Materialy III Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (Sterlitamak, 4–6 dekabrya 2014 g.), RIZO Sterlitamakskogo filiala BashGU, Sterlitamak, 2014, 115–117
68.
F. Kh .Mukminov, V. F. Gilimshina, “Teklindovskie klassy edinstvennosti dlya neravnomerno parabolicheskogo uravneniya”, Tretya mezhdunarodnaya konferentsiya "Matematicheskaya fizika i ee prilozheniya (Samara, 27 avgusta–1 sentyabrya 2012g.), SamGTU, Samara, 2012, 96–97
69.
F. Kh. Mukminov, E. R. Andriyanova, “O suschestvovanii resheniya parabolicheskogo uravneniya s dvoinoi nelineinostyu v neogranichennykh oblastyakh”, International conference dedicated to Ivan G. Petrovskii (Moskow, May 30-June 4 2011), Izd-vo MGU, Moskva, 2011, 136–137
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