01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
Keywords:
integro-differential equation, inverse problem, the wave equation, pulse source, the characteristic,
uniqueness, estimate of stability
Subject:
Inverse problems for hyperbolic equations
with memory Inverse problems for integro--differential equations of hyperbolic and parabolic types
Main publications:
1.Durdiev.D.K. On correctness of one inverse problem for the hyperbolic integro-differential
equation//Sib.Math.Journ. 33(1992),3, p.69-77(in russion).
2.Durdiev.D.K. A multi-dimensional inverse problem for equation with memory.//Sib.Math.Journ. 35(1994),3, p.574-582(in russion).
D. K. Durdiev, “Coefficient inverse problem for an equation of mixed parabolic-hyperbolic type with a non-characteristic line of type change”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 3, 38–49
2.
D. K. Durdiev, “Unknown coefficient problem for mixed equation of parabolic-hyperbolic type with non-local boundary conditions on characteristics”, Ufimsk. Mat. Zh., 16:2 (2024), 82–88; Ufa Math. J., 16:2 (2024), 81–88
3.
D. K. Durdiev, T. R. Suyarov, “Inverse coefficient problem for the 2D wave equation with initial and nonlocal boundary conditions”, Vladikavkaz. Mat. Zh., 26:2 (2024), 5–25
4.
D. K. Durdiev, I. I. Hasanov, “Inverse coefficient problem for a partial differential equation with multi-term orders fractional Riemann–Liouville derivatives”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 34:3 (2024), 321–338
2023
5.
D. K. Durdiev, Kh. Kh. Turdiev, “The problem of finding the kernels in the system of integro-differential acoustics equations”, Dal'nevost. Mat. Zh., 23:2 (2023), 190–210
6.
Durdimurod K. Durdiev, Asliddin A. Boltaev, “The problem of determining kernels in a two-dimensional system of viscoelasticity equations”, Bulletin of Irkutsk State University. Series Mathematics, 43 (2023), 31–47
7.
D. K. Durdiev, A. A. Boltaev, A. A. Rahmonov, “Convolution kernel determination problem in the third order Moore–Gibson–Thompson equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 12, 3–16
D. K. Durdiev, J. Z. Nuriddinov, “Uniqueness of the kernel determination problem in an integro-differential parabolic equation with variable coefficient”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 11, 3–14
9.
D. K. Durdiev, J. J. Jumaev, “Inverse problem of determining the kernel of integro-differential fractional diffusion equation in bounded domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 10, 22–35
10.
D. K. Durdiev, J. Sh. Safarov, J. Sh. Safarov, “Inverse Problem for an Integrodifferential Equation of the Hyperbolic Type protect in a Rectangular Domain”, Mat. Zametki, 114:2 (2023), 244–259; Math. Notes, 114:2 (2023), 199–211
D. K. Durdiev, J. J. Jumaev, D. D. Atoev, “Inverse problem on determining two kernels in integro-differential equation of heat flow”, Ufimsk. Mat. Zh., 15:2 (2023), 120–135; Ufa Math. J., 15:2 (2023), 119–134
Durdimurod K. Durdiev, Zhavlon Z. Nuriddinov, “Kernel determination problem for one parabolic equation with memory”, Ural Math. J., 9:2 (2023), 86–98
13.
D. K. Durdiev, “Inverse problem for an equation of mixed parabolic-hyperbolic type with a characteristic line of change”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 27:4 (2023), 607–620
14.
D. K. Durdiev, Z. R. Bozorov, A. A. Boltayev, “Inverse problem for the system of viscoelasticity in anisotropic media with tetragonal form of elasticity modulus”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:4 (2023), 581–600
15.
D. K. Durdiev, J. J. Jumayev, D. D. Atoev, “Letter to the Editor: Correction to the “Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition” [Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2023, vol. 33, issue 1, pp. 90-102]”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:2 (2023), 382–384
16.
D. K. Durdiev, J. J. Jumayev, D. D. Atoev, “Kernel determination problem in an integro-differential equation of parabolic type with nonlocal condition”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 90–102
Durdimurod K. Durdiev, Zhanna D. Totieva, “Determination of non-stationary potential analytical with respect to spatial variables”, J. Sib. Fed. Univ. Math. Phys., 15:5 (2022), 565–576
18.
D. K. Durdiev, Zh. D. Totieva, “Determination of a non-stationary adsorption coefficient analytical in part of spatial variables”, Mat. Tr., 25:2 (2022), 88–106; Siberian Adv. Math., 33:1 (2023), 1–14
19.
D. K. Durdiev, Sh. B. Merajova, “Inverse problem for an equation of mixed parabolic-hyperbolic type with a Bessel operator”, Sib. Zh. Ind. Mat., 25:3 (2022), 14–24
20.
D. K. Durdiev, J. Sh. Safarov, “2D kernel identification problem in viscoelasticity equation with a weakly horizontal homogeneity”, Sib. Zh. Ind. Mat., 25:1 (2022), 14–38
D. K. Durdiev, “Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 26:2 (2022), 355–367
D. K. Durdiev, J. Sh. Safarov, “The problem of determining the memory of an environment with weak horizontal heterogeneity”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:3 (2022), 383–402
D. K. Durdiev, E. L. Shishkina, S. M. Sitnik, “Fractional powers of Bessel operator and its numerical calculation”, Chelyab. Fiz.-Mat. Zh., 6:2 (2021), 172–189
25.
Durdimurod K. Durdiev, Zhavlon Z. Nuriddinov, “Determination of a multidimensional kernel in some parabolic integro–differential equation”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 117–127
D. K. Durdiev, K. K. Turdiev, “The problem of finding the kernels in the system
of integro-differential Maxwell's equations”, Sib. Zh. Ind. Mat., 24:2 (2021), 38–61; J. Appl. Industr. Math., 15:2 (2021), 190–211
D. K. Durdiev, Zh. D. Totieva, “About global solvability of a multidimensional inverse problem for an equation with memory”, Sibirsk. Mat. Zh., 62:2 (2021), 269–285; Siberian Math. J., 62:2 (2021), 215–229
D. K. Durdiev, Zh. D. Totieva, “Inverse problem for a second-order hyperbolic integro-differential equation with variable coefficients for lower derivatives”, Sib. Èlektron. Mat. Izv., 17 (2020), 1106–1127
D. K. Durdiev, A. A. Rahmonov, “The problem of determining the 2D-kernel in a system of integro-differential equations of a viscoelastic porous medium”, Sib. Zh. Ind. Mat., 23:2 (2020), 63–80; J. Appl. Industr. Math., 14:2 (2020), 281–295
D. K. Durdiev, Zh. Z. Nuriddinov, “On investigation of the inverse problem for a parabolic integro-differential equation with a variable coefficient of thermal conductivity”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:4 (2020), 572–584
Zh. D. Totieva, D. K. Durdiev, “The Problem of Finding the One-Dimensional Kernel of the Thermoviscoelasticity Equation”, Mat. Zametki, 103:1 (2018), 129–146; Math. Notes, 103:1 (2018), 118–132
D. K. Durdiev, A. A. Rakhmonov, “Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability”, TMF, 195:3 (2018), 491–506; Theoret. and Math. Phys., 195:3 (2018), 923–937
D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional kernel of the electroviscoelasticity equation”, Sibirsk. Mat. Zh., 58:3 (2017), 553–572; Siberian Math. J., 58:3 (2017), 427–444
D. K. Durdiev, U. D. Durdiev, “The problem of kernel determination from viscoelasticity system integro-differential equations for homogeneous anisotropic media”, Nanosystems: Physics, Chemistry, Mathematics, 7:3 (2016), 405–409
D. K. Durdiev, Zh. Sh. Safarov, “Inverse Problem of Determining the One-Dimensional Kernel of the Viscoelasticity Equation in a Bounded Domain”, Mat. Zametki, 97:6 (2015), 855–867; Math. Notes, 97:6 (2015), 867–877
D. K. Durdiev, “Inverse problem for the identification of a memory kernel from Maxwell's system integro-differential equations for a homogeneous anisotropic media”, Nanosystems: Physics, Chemistry, Mathematics, 6:2 (2015), 268–273
D. Q. Durdiev, Zh. D. Totieva, “The problem of determining the multidimensional kernel of viscoelasticity equation”, Vladikavkaz. Mat. Zh., 17:4 (2015), 18–43
D. K. Durdiev, “On the uniqueness of kernel determination in the integro-differential equation of parabolic type”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:4 (2015), 658–666
D. K. Durdiev, Z. R. Bozorov, “A problem of determining
the kernel of integrodifferential wave equation with weak
horizontal properties”, Dal'nevost. Mat. Zh., 13:2 (2013), 209–221
D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional kernel of the viscoelasticity equation”, Sib. Zh. Ind. Mat., 16:2 (2013), 72–82
D. K. Durdiev, Zh. Sh. Safarov, “The local solvability of a problem of determining the spatial part of a multidimensional kernel in the integro-differential equation of hyperbolic type”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(29) (2012), 37–47
Durdimurod K. Durdiev, “An Identification Problem of Memory Function of a Medium and the Form of an Impulse Source”, J. Sib. Fed. Univ. Math. Phys., 2:2 (2009), 127–136
D. K. Durdiev, “The Problem of Determining a Function of the Memory of a Medium and of the Regular Part of a Pulsed Source”, Mat. Zametki, 86:2 (2009), 202–212; Math. Notes, 86:2 (2009), 187–195
44.
D. K. Durdiev, “An Inverse Problem for Determining Two Coefficients in an Integrodifferential Wave Equation”, Sib. Zh. Ind. Mat., 12:3 (2009), 28–40
D. K. Durdiev, “Global solvability of two unknown variables identification problem in one inverse problem for the integro-differential wave equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(19) (2009), 17–28
2008
46.
D. K. Durdiev, “Problem of determining the nonstationary potential in a hyperbolic-type equation”, TMF, 156:2 (2008), 220–225; Theoret. and Math. Phys., 156:2 (2008), 1154–1158
D. K. Durdiev, “A multidimensional inverse problem for an equation with memory”, Sibirsk. Mat. Zh., 35:3 (1994), 574–582; Siberian Math. J., 35:3 (1994), 514–521
D. K. Durdiev, “On the ill-posedness of an inverse problem for a hyperbolic integro-differential equation”, Sibirsk. Mat. Zh., 33:3 (1992), 69–77; Siberian Math. J., 33:3 (1992), 427–433