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1

Source term model for elasticity system with nonlinear dissipative term in a thin domain

Dilmi Mohamed, Dilmi Mourad, Boulaaras Salah, Benseridi Hamid

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

437--451

EN

This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u∗ is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.

2

Fast growing solutions to linear differential equations with entire coefficients having the same ρϕ-order

Belaϊdi Benharrat

Journal of Mathematics and Applications

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2019

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Vol. 42

63--77

EN

This paper deals with the growth of solutions of a class of higher order linear differential equations f(k)+Ak-1(z)f(k-1)+ … +A1(z)f’+A0(z)f=0; k≥2 when most coefficients Aj (z) (j = 0, ..., k-1) have the same ρϕ-order with each other. By using the concept of τϕ-type, we obtain some results which indicate growth estimate of every non-trivial entire solution of the above equations by the growth estimate of the coefficient A0 (z). We improve and generalize some recent results due to Chyzhykov-Semochko and the author.

3

The poles method for second-order linear time-varying systems

Siwczyński M., Jaraczewski M.

Czasopismo Techniczne. Mechanika

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2015

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Y. 112, iss. 4-M

123--130

EN

In dynamic linear systems described by differential equations with constant parameters, the poles of the rational function (transfer function of the system) play an important role. This article attempts to expand the poles concept in a situation where the system is described by the second-order linear system with timevarying parameters. It then introduces the concept of characteristic equations and time-dependent poles.

PL

W opisie liniowych systemów dynamicznych opisanych przez równania różniczkowe o stałych parametrach ważną rolę odgrywają bieguny funkcji wymiernej (transmitancji systemu). Ten artykuł rozszerza koncepcję biegunów na przypadek, gdy system jest opisany równaniem liniowym drugiego rzędu o zmiennych w czasie parametrach. Pojawiają się tu pojęcia zależnego od czasu równania charakterystycznego i zależnych od czasu biegunów transmitancji.

4

The poles method for higher-order linear time-varying systems

Siwczyński M., Jaraczewski M.

Czasopismo Techniczne. Mechanika

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2015

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Y. 112, iss. 4-M

117--122

EN

In dynamic linear systems described by differential equations with constant parameters, the poles of the rational function (transfer function of the system) play an important role. This article attempts to expand the poles concept in a situation where the system is described by the N-th order linear system with time-varying parameters. It then introduces the concept of characteristic equations and time-dependent poles.

PL

W opisie liniowych systemów dynamicznych opisanych przez równania różniczkowe o stałych parametrach ważną rolę odgrywają bieguny funkcji wymiernej (transmitancji systemu). Ten artykuł rozszerza koncepcję biegunów na przypadek, gdy system jest opisany równaniem liniowym N-tego rzędu o zmiennych w czasie parametrach. Pojawia się tu pojęcie zależnego od czasu równania charakterystycznego i zależnych od czasu biegunów transmitancji.

5

Properties of higher order differential polynomials generated by solutions of complex differential equations in the unit disc

Latreuch Z., Belaidi B.

Journal of Mathematics and Applications

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2014

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Vol. 37

67--84

EN

The main purpose of this paper is to study the controllability of solutions of the differential equation [...] In fact, we study the growth and oscillation of higher order differential polynomial with meromorphic coefficients in the unit disc [...] generated by solutions of the above kth order differential equation.

6

The frequency of the zeros of some differential polynomials

Belaïdi B.

Demonstratio Mathematica

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2013

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Vol. 46, nr 1

75--86

EN

Let ρp(ƒ) and σp(ƒ) denote respectively the iterated p-order and the iterated p-type of an entire function ƒ. In this paper, we study the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation f''+A1(z)f'+A0(z)f=0 where A1(z), A0(z) are entire functions of finite iterated p-order such that ρp(A1) = ρp(A0) = ρ(0< ρ <+∞) and σp(A1)< σp(A0) =σ(0< σ <+∞).

7

Oscillation on the left and on the right

Ohriska J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2009

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Vol. 14

87-95

EN

In the present paper we derive sufficient conditions for the linear differential equation (r(t)y′(t))′+p(t)y(t) = 0 to be either oscillatory or non-oscillatory on the left and eventually on the right. Some estimations of count of zero point s for solutions to considered equation on an interval are also presented.

8

Heat-balance integral method in solidification problems involving small spatial perturbations

Pauk V.

Journal of Technical Physics

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2000

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Vol. 41, no 1

65-74

EN

The heat-balance integral method is applied to solve the solidification problem involving a small spatial periodic fluctuations in the mold temperature. These initial irregularities lead to perturbations in the temperature field and the planar solidification line. The problem is reduced to linear differential equations for amplitudes of the interface perturbations and solutions are presented in closed forms. The numerical analysis is performed for a sinusoidal perturbation. Presented results show the oscillations in the solidification front as a function of time and parameters of the problem. The stability of an interface between solid and liquid phases is investigated.