05.13.18; 05.13.17 (Mathematical modeling, numerical methods, and the program systems; Theoretical foundation for informatics)
Birth date:
7.10.1950
E-mail:
Keywords:
Sobolev-type equations, solution blow-up, existence of a global solution
Subject:
Linear and nonlinear equations of Sobolev type, Cauchy problem, Goursat problem, Riemann method
Main publications:
1. Kh. G. Umarov, “The Riemann method for some hyperbolic equations with constant operator coefficients”, Dokl. AN SSSR, 259:3 (1981), 549 – 553.
2. Kh. G. Umarov, “The Cauchy problem in a Banach space for an analogue of the diffusion equation that is not solved with respect to the time derivative”, Dokl. AN SSSR, 314:6 (1990) 1352–1356.
3. Kh. G. Umarov, Operator semigroups and exact solutions of anisotropic filtering problems, Fizmatlit, Moscow, 2009, 216 pp.
4. Umarov Kh. G., “The Cauchy problem for the equation of torsional vibrations of a nonlinearly elastic rod of infinite length”, Prikl. math. i Mech., 83:2 (2019), 249–264
Kh. G. Umarov, “Blow-up of the solution to the equation for nonlinear beam vibrations with allowance for transverse deformation effects”, Zh. Vychisl. Mat. Mat. Fiz., 63:11 (2023), 1877–1893; Comput. Math. Math. Phys., 63:11 (2023), 2107–2122
2.
Kh. G. Umarov, “Solution blow-up and global solvability of the Cauchy problem for the equation of moderately long longitudinal waves in a viscoelastic rod”, Zh. Vychisl. Mat. Mat. Fiz., 63:7 (2023), 1177–1191; Comput. Math. Math. Phys., 63:7 (2023), 1285–1299
2022
3.
Kh. G. Umarov, “Blow-up and global solvability of the Cauchy problem for a pseudohyperbolic equation related to the generalized Boussinesq equation”, Sibirsk. Mat. Zh., 63:3 (2022), 672–689; Siberian Math. J., 63:3 (2022), 559–574
Kh. G. Umarov, “The Cauchy problem for the nonlinear long longitudinal waves equation in a viscoelastic rod”, Sibirsk. Mat. Zh., 62:1 (2021), 198–209; Siberian Math. J., 62:1 (2021), 159–168
Kh. G. Umarov, “The Cauchy problem for the equation of bending vibrations of a nonlinear-elastic rod of infinite length”, Vladikavkaz. Mat. Zh., 19:3 (2017), 59–69
2013
6.
Kh. G. Umarov, “Solvability of the Cauchy problem for the Aller equation in space of bounded continuous functions”, Vladikavkaz. Mat. Zh., 15:4 (2013), 65–75
Kh. G. Umarov, “Explicit solution of the mixed problem in an anisotropic half-space for the Barenblatt–Zheltov–Kochina equation”, Vladikavkaz. Mat. Zh., 15:1 (2013), 51–64
Kh. G. Umarov, “Explicit solution of Cauchy problem for the linearized system of phase field equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(26) (2012), 256–260
9.
Kh. G. Umarov, “Explicit solution of the mixed problem in anisotropic semispace with brightly expressed vertical permeability for Barenblatt–Zheltov–Kochina equation”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, no. 6(97), 75–99
2011
10.
Kh. G. Umarov, “Explicit solution of the Cauchy problem to the equation for groundwater motion with a free surface”, Ufimsk. Mat. Zh., 3:2 (2011), 81–86; Ufa Math. J., 3:2 (2011), 79–84
1992
11.
Kh. G. Umarov, “A mixed problem in a Banach space for an analogue of the diffusion equation that is not solved with respect to the time derivative”, Izv. Vyssh. Uchebn. Zaved. Mat., 1992, no. 4, 100–103; Russian Math. (Iz. VUZ), 36:4 (1992), 98–101
Kh. G. Umarov, “The Cauchy problem in a Banach space for an analogue of a
diffusion equation that is not solved with respect to the time
derivative”, Dokl. Akad. Nauk SSSR, 314:6 (1990), 1352–1356; Dokl. Math., 42:2 (1991), 693–697
1982
13.
Kh. G. Umarov, “Solution by Riemann's method of the Goursat problem for certain hyperbolic equations with variable operator coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 12, 76–79
1981
14.
Kh. G. Umarov, “Riemann's method for some hyperbolic equations with constant operator coefficients”, Dokl. Akad. Nauk SSSR, 259:3 (1981), 549–553
2023
15.
O. G. Avsyankin, S. N. Askhabov, B. G. Vakulov, V. S. Guliev, I. M. Erusalimskyi, A. N. Karapetyants, G. S. Rostetskaya, A. G. Kusraev, N. G. Samko, S. G. Samko, Kh. G. Umarov, A. F. Chuvenkov, “Salaudin Musaevich Umarkhadzhiev (on the occasion of his 70th birthday)”, Vladikavkaz. Mat. Zh., 25:1 (2023), 141–142
2021
16.
A. V. Abanin, O. G. Avsyankin, V. I. Burenkov, B. G. Vakulov, S. K. Vodopyanov, M. L. Gol'dman, V. S. Guliev, I. M. Erusalimskyi, A. N. Karapetyants, M. I. Karyakin, V. M. Kokilashvili, A. G. Kusraev, E. R. Liflyand, A. V. Pskhu, V. S. Rabinovich, S. V. Rogozin, B. S. Rubin, A. P. Soldatov, I. M. Spitkovsky, V. D. Stepanov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Stefan Grigorievich Samko (on the occasion of his 80th birthday)”, Vladikavkaz. Mat. Zh., 23:3 (2021), 126–129
2017
17.
A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Alexey Borisovich Shabat (on his 80's anniversary)”, Vladikavkaz. Mat. Zh., 19:3 (2017), 83–85
2012
18.
A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Shabat Aleksei Borisovich (on his 75th birthday)”, Vladikavkaz. Mat. Zh., 14:2 (2012), 71–73
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