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Abstract  

We consider a system consisting of a quasilinear parabolic equation and a first order ordinary differential equation where both equations contain functional dependence on the unknown functions. Then we consider a system which consists of a quasilinear parabolic partial differential equation, a first order ordinary differential equation and an elliptic partial differential equation. These systems were motivated by models describing diffusion and transport in porous media with variable porosity.

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Abstract  

This paper is a review of recent developments of a research line proposed on the turn of the decades, 1980s to 1990s. The main results concern basic qualitative properties of nonlinear models of population biology, such as controllability and observability. The methods applied are different for the density-dependent models of population ecology and for the frequency-dependent models of population genetics and evolutionary theory. While in the first case the classical theorems of nonlinear systems theory can be used, in the second one an extension of classical results to systems with invariant manifold is necessary.

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Abstract  

We consider a system consisting of a first order differential equation, a parabolic and an elliptic equation. Existence of weak solutions is proved by using the Schauder fixed point theorem. The paper improves some results of [3, 6] which is illustrated by example

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system identification in 100 exercises , Wiley-IEEE Press, 2012. Schetzen M. The Volterra and Wiener theories of nonlinear systems , John Wiley & Sons, NY, USA, 1980

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_dinamikus_rendszerek/index.html (last visited 12 November 2017). [15] Khalil H. K. Nonlinear systems , Prentice Hall, 1999

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The paper presents the numerical modeling of a Y-shaped three-pole radial magnetic bearing based on two-dimensional (2D) and three-dimensional (3D) magnetic field computation with nonlinear model of the material. The used numerical method is the Finite Element Method (FEM). The nonlinear system of equations according to the nonlinear characteristics of ferromagnetic material can be handled by the Newton-Raphson technique and by the fixed-point method.

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This paper deals with the numerical analysis of a vector hysteresis measurement system, which is under construction in the laboratory. The aim is to build up a single sheet tester with round shaped specimen. The goal of simulations is to find out the main features of the measurement system. The 3D finite element method (FEM) with tetrahedral mesh developed in the laboratory has been applied for investigations of the nonlinear eddy current field problem. The characteristic of the magnetic material has been taken into account by the isotropic vector Preisach model. The nonlinearity has been handled by the polarization method and the nonlinear system of equations has been solved by the fixed-point technique. The first results are presented in this work.

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identity for half-linear differential equations, (to appear). MIRZOV, J. D., Principal and nonprincipal solutions of a nonlinear system, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 31 (1988), 100-117. MR 91a :34010

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