Browsing by Author "Shakhmurov,V."

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Citation Count: 0
The dynamics of a cancer tumor growth model with multiphase structure
(International Institute of Informatics and Systemics, IIIS, 2018) Shakhmurov,V.; Shahmurov,R.
In this paper, we studied a phase-space analysis of a mathematical model of tumor growth with an im- mune responses. Mathematical analysis of the model equations with multipoint initial condition, regarding to dissipativity, boundedness of solutions, invari- ance of non-negativity, nature of equilibria, local and global stability have been investigated. We studied some features of behavior of one of three-dimensional tumor growth models with dynamics described in terms of densities of three cells populations: tumor cells, healthy host cells and effector immune cells. We found sufficient conditions, under which trajectories from the positive domain of feasible multipoint initial conditions tend to one of equilibrium points. Here, cases of the small tumor mass equilibrium points-the healthy equilibrium point, the death equilibrium point have been examined. Biological implications of our results are discussed. © WMSCI 2018 - 22nd World Multi-Conference on Systemics, Cybernetics and Informatics, Proceedings. All rights reserved.
Citation Count: 0
Fractional differential operators in vector–valued spaces and applications
(Element D.O.O., 2020) Shakhmurov,V.
Fractional differential operator equations with parameter are studied. Uniform Lpseparability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives. Moreover, maximal regularity properties of the fractıonal abstract parabolic equation are established. Particularly, it is proven that the operators generated by these equations are positive and also are generators of analytic semigroups. As an application, the anisotropic parameter dependent fractional differential equations and the system of fractional differential equations are studied. © 2020 Element D.O.O.. All rights reserved.
Citation Count: 13
MAXIMAL REGULAR CONVOLUTION-DIFFERENTIAL EQUATIONS IN WEIGHTED BESOV SPACES
(Institute of Applied Mathematics of Baku State University, 2017) Shakhmurov,V.; Musaev,H.
By using Fourier multiplier theorems, the maximal regularity properties of abstract convolution differential equations in weighted Besov spaces are investigated. It is shown that the corresponding convolution differential operators are positive and generate analytic semi-groups in abstract Besov spaces. Then, the well-posedness of the Cauchy problem for parabolic convolution–operator equation is established. Moreover, these results are used to establish maximal regularity properties for system of integro-differential equations of finite and infinite orders. © 2017, Institute of Applied Mathematics of Baku State University. All rights reserved.
Citation Count: 8
Sectorial operators with convolution term
(Element D.O.O., 2010) Shakhmurov,V.; Shahmurov,R.
In the present paper, separability properties of convolution-differential equations with unbounded operator coefficients in Banach valued Lp spaces are investigated. A coercive estimate for resolvent of corresponding realization operator, especially, its R-sectoriality is obtained. Finally, these results applied to establish maximal regularity of Cauchy problem for the abstract parabolic convolution equations and integro-differential equations on infinite dimension state spaces. © ELEMENT, Zagreb.
Citation Count: 8
Separability properties of convolution-differential operator equations in weighted Lp spaces
(Azerbaijan National Academy of Sciences, 2015) Shakhmurov,V.; Musaev,H.
In the present paper, separability properties of convolution - differential operator equations with unbounded operator coefficients in Banach space-valued weighted Lp-class are investigated. The coercive estimate for resolvent of the corresponding realization operator, especially its R - positivity is obtained. Finally, these results an applied to establish wellposedeness of the Cauchy problem for the abstract parabolic convolution equations and system of finite and infinite order integro-differential equations. © 2015, Azerbaijan National Academy of Sciences. All rights reserved.