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Slabá řešení pro třídu nelineárních integrodiferenciálních rovnic
Soukup, Ivan ; Bárta, Tomáš (advisor) ; Kaplický, Petr (referee)
Title: Weak solutions for a class of nonlinear integrodifferential equations Author: Ivan Soukup Department: Department of mathematical analysis Supervisor: RNDr. Tomáš Bárta, Ph.D. Supervisor's e-mail address: tomas.barta@mff.cuni.cz Abstract: The work investigates a system of evolutionary nonlinear partial integrodifferential equations in three dimensional space. In particular it stud- ies an existence of a solution to the system introduced in [1] with Dirichlet boundary condition and initial condition u0. We adopt the scheme of the proof from [9] and try to avoid the complications rising from the integral term. The procedure consists of an approximation of the convective term and an ap- proximation of the potentials of both nonlinearities using a quadratic function, proving the existence of the approximative solution and then returning to the original problem via regularity of the approximative solution and properties of the nonlinearities. The aim is to improve the results of the paper [1]. 1
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Slabá řešení pro třídu nelineárních integrodiferenciálních rovnic
Soukup, Ivan ; Bárta, Tomáš (advisor) ; Kaplický, Petr (referee)
Title: Weak solutions for a class of nonlinear integrodifferential equations Author: Ivan Soukup Department: Department of mathematical analysis Supervisor: RNDr. Tomáš Bárta, Ph.D. Supervisor's e-mail address: tomas.barta@mff.cuni.cz Abstract: The work investigates a system of evolutionary nonlinear partial integrodifferential equations in three dimensional space. In particular it stud- ies an existence of a solution to the system introduced in [1] with Dirichlet boundary condition and initial condition u0. We adopt the scheme of the proof from [9] and try to avoid the complications rising from the integral term. The procedure consists of an approximation of the convective term and an ap- proximation of the potentials of both nonlinearities using a quadratic function, proving the existence of the approximative solution and then returning to the original problem via regularity of the approximative solution and properties of the nonlinearities. The aim is to improve the results of the paper [1]. 1
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To the analysis of the bearing stiffness influence on the amplitude frequency characteristic of the gear wheels
Hortel, Milan ; Škuderová, Alena
To the analysis of the bearing stiffness influence on the amplitude frequency characteristic of the gear wheels.This contribution deals with the theory of planar steady damped oscillation of the isolated pair of spur gear, which is in two orthogonal direction elastically suspended. The analysis of the periodical solution was carried out by means of transformation of the differential boundary-value problem to the integral problem with the successive approximation and simulation method. The purpose is the determination of the bearing stiffness influence on the dynamic force in gearing mesh.
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