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Registration Number

0219U100306, 0118U003795 , R & D reports

Title

Geometric properties of metric spaces, dynamical systems and features parabolic equations.Then second year of impiementation.

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Head

Koliadа Serhii F., Доктор фізико-математичних наук

Registration Date

05-02-2019

Organization

Department for special training National academy of science of Ukraine at Kiev University

Description

 Localized regimes with singular peaking for quasilinear parabolic equations were studied. A precise estimate of solutions of the mentioned problems has been obtained. There were studied asymptotic properties of large solutions of a wide class of quasilinear parabolic equations of the dissusion-nonlinear degenerate absorption type. The law of coexistence of homoclinic trajectories to cycles of different periods of the continuous mappings of a segment is determined. The connection between the coexistence of periodic and homoclinic trajectories for perturbed multidimensional and unperturbed one-dimensional dynamical systems is investigated. We introduce and investigate ordinal spaces, which in some sense are generalizations of semi-metric spaces. The isomorphism conditions for ordinal spaces and the isomorphism conditions for the Hasse diagrams of the balleans of finite ordinal spaces were found. The question of the embedding of ordinal spaces into real line and into Euclidean spaces of higher dimensions is investigated. Through a continuity module we obtain new estimates for polynomials that approximate a continuous on interval function. The behavior of such polynomials is studied, a pointwise estimates for the value of the approximation for them are obtained.

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