Browsing by Author "Shahmurov,R."

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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: 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.