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
2021
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
2020
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
2019
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
2018
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
2021
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
2018
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
2017
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
2019
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
2017
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.
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
18.
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
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
24.
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
25.
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
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
2015
28.
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
2014
29.
E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. Journal, 6:4 (2014), 31–47
30.
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
31.
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
2013
32.
V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597
33.
È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Sb. Math., 204:9 (2013), 1239–1263
2012
34.
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
35.
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
2011
36.
V. F. Gilimshina, F. Kh. Mukminov, “On the decay of solutions of non-uniformly elliptic equations”, Izv. Math., 75:1 (2011), 53–71
37.
V. F. Gilimshina, F. Kh. Mukminov, “On decay rate of solution to degenerating linear parabolic equations”, Ufimsk. Mat. Zh., 3:4 (2011), 43–56
38.
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
39.
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
40.
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
2010
41.
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
2009
42.
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
F. Kh. Mukminov, I. M. Bikkulov, “Ob ubyvanii reshenii zadachi Rikke dlya ellipticheskikh uravnenii chetvertogo poryadka v neogranichennoi oblasti”, Mezhdunarodnaya konferentsiya, posvyaschennaya pamyati I. G. Petrovskogo, Tezisy dokladov (Moskva, 2007), Izd-vo MGU, Moskva, 2007, 187
45.
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
2008
46.
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
2004
47.
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
2002
48.
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
2001
49.
A. A. Bormisov, F. Kh. Mukminov, “Symmetries of Systems of the Hyperbolic Riccati Type”, Theoret. and Math. Phys., 127:1 (2001), 446–459
2000
50.
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
51.
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
1997
52.
F. Kh. Mukminov, “On the set of limit functions for solutions of the nonstationary exterior Stokes problem”, Differ. Equ., 33:8 (1997), 1108–1112
53.
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
54.
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
55.
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
56.
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
1996
57.
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
58.
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
59.
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
1995
60.
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
1994
61.
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
62.
F. Kh. Mukminov, “Uniform stabilization of the solutions of the exterior problem for Navier–Stokes equations”, Dokl. Math., 48:2 (1994), 248–250
1992
63.
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
1994
64.
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
1992
65.
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
66.
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
1988
67.
F. Kh. Mukminov, “On straightening the characteristics of a quasilinear second-order equation”, Theoret. and Math. Phys., 75:1 (1988), 340–345
1987
68.
F. Kh. Mukminov, Differ. Uravn., 23:10 (1987), 1772–1780
1988
69.
F. Kh. Mukminov, V. V. Sokolov, “Integrable evolution equations with constraints”, Math. USSR-Sb., 61:2 (1988), 389–410
1981
70.
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
1979
71.
F. Kh. Mukminov, Differ. Uravn., 15:11 (1979), 2021–2033
2023
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