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1
Hydromagnetic effects on non-Newtonian Hiemenz flow
Sarkar Suman, Sahoo Bikash
Journal of Applied Analysis
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2022
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Vol. 28, nr 1
95--104
EN
The stagnation point flow of a non-Newtonian Reiner-Rivlin fluid has been studied in the presence of a uniform magnetic field. The technique of similarity transformation has been used to obtain the selfsimilar ordinary differential equations. In this paper, an attempt has been made to prove the existence and uniqueness of the solution of the resulting free boundary value problem. Monotonic behavior of the solution is discussed. The numerical results, shown through a table and graphs, elucidate that the flow is significantly affected by the non-Newtonian cross-viscous parameter L and the magnetic parameter M.
2
Existence of solutions of BVPs for fractional Langevin equations involving Caputo fractional derivatives
Kiyamehr Zohre, Baghani Hamid
Journal of Applied Analysis
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2021
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Vol. 27, nr 1
47--55
EN
This article investigates a nonlinear fractional Caputo-Langevin equation Dβ(Dα + λ)x(t) = f(t, x(t)), 0 < t < 1, 0 < α ≤ 1, 1 < β ≤ 2, subject to the multi-point boundary conditions x(0) = 0, D2αx(1) + λDαx(1) = 0, x(1) =η∫0 x(τ) dτ for some 0 < η < 1, where Dα is the Caputo fractional derivative of order α, f : [0, 1] × ℝ → ℝ is a given continuous function, and λ is a real number. Some new existence and uniqueness results are obtained by applying an interesting fixed point theorem.
3
Existence and uniqueness of a problem in thermo-elasto-plasticity with phase transitions in TRIP steels under mixed boundary conditions
Boettcher S.
Journal of Applied Analysis
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2018
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Vol. 24, nr 1
87--98
EN
In this paper a complex model describing thermo-elasto-plasticity, phase transitions (PT) and transformation-induced plasticity (TRIP) is studied. The main objective is the analysis of the corresponding initial and boundary value problem (IBVP) considering linearized thermo-elastic dissipation and a viscosity-like regularization.
4
Content available Damped solutions of singular IVPS with Φ-Laplacian
Stryja J.
Systemy Wspomagania w Inżynierii Produkcji
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2017
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Vol. 6, iss. 4
306--313
EN
We study analytical properties of a singular nonlinear ordinary differential equation with a Φ-Laplacian. We investigate solutions of the initial value problem (p(t)Φ(u’(t)))’ + p(t)f(Φ(u(t))) = 0, u(0) = uₒ ϵ [Lₒ,L], u’(0) = 0 on the half-line [0,∞). Here, f is a continuous function with three zeros, function p is positive on (0,∞) and p(0) = 0. The integral ∫₀1dsds/p(s) may be divergent which yields the time singularity at t = 0. Our equation generalizes equations which appear in hydrodynamics or in the nonlinear field theory.
CS
Budeme se zabývat chováním rešení singulární obycejné diferenciální rovnice druhého rádu s Φ-Laplaciánem (p(t)Φ(u’(t)))’ + p(t)f(Φ(u(t))) = 0, u(0) = uₒ ϵ [Lₒ,L], u’(0) = 0 na poloprímce [0, ∞) za pocátecních podmínek u(0) = uₒ ϵ [Lₒ,L], u’(0) = 0 Funkce f je spojitá a má tri nulové body, funkce p je kladná na (0,1)a dále platí p(0) = 0. Integrál ∫₀1ds/p(s)) muže být divergentní, což zpusobuje singularitu v t = 0. Naše rovnice zobecnuje rovnice vyskytující se v modelech napríklad v hydrodynamice nebo v nelineární teorii pole.
5
Content available remote Uniqueness results for fredholm type Fractional order Riemann-Liouville integral equations
Abbas S., Benchohra M.
Fasciculi Mathematici
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2013
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Nr 51
5--19
EN
In this paper we study the existence and uniqueness of solutions of a certain Fredholm type Riemann-Liouville integral equation of two variables by using Banach contraction principle.
6
On a nonlinear dynamic integrodifferential equation on time scales
Pachpatte D. B.
Journal of Applied Analysis
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2010
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Vol. 16, nr 2
279-294
EN
The main objective of the present paper is to study some basic qualitative properties of solutions of a certain nonlinear integrodifferential equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain inequality with explicit estimate on time scales.
7
Content available remote Integral equation arising in the theory of partial differential equations
Pachpatte B. G.
Fasciculi Mathematici
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2010
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Nr 43
115-126
EN
The aim of the present paper is to study some basic qualitative properties of solutions of a certain integral equation arising in the theory of partial differential equations. The well known Banach fixed point theorem and the new integral inequality with explicit estimate obtained in the present paper are used to establish the results.
8
Content available remote Solvability conditions for a nonlocal boundary value problem for linear functional differential equations
Lomtatidze A., Opluštil Z., Šremr J.
Fasciculi Mathematici
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2009
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Nr 41
81-96
9
Content available remote Functional differential equations of second order
Skóra L.
Czasopismo Techniczne. Nauki Podstawowe
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2009
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R. 106, z. 1-NP
63-75
EN
In this article, we present some results on the existence and uniqueness of the solutions of boundary value problem for functional differential equations of second order.
PL
Artykuł zawiera wyniki dotyczące istnienia i jednoznaczności rozwiązań zagadnienia brzegowego dla równań różniczkowo-funkcjonalnych drugiego rzędu.
10
Content available remote A shock problem involving a nonlinear viscoelastic bar associated with a nonlinear boundary condition
Long N., Giai V., Truong L.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
85-108
EN
We study the initial-boundary value problem for a nonlinear wave equation given by [...] where p > 2, q > l, K, lambda are given constants and uo, u1, F are given functions, the unknown function u(x,t) and the unknown boundary value P (t) satisfy the following nonlinear integral equation [...] where K1, alpha, beta are given constants and g, k arę given functions. In Part 1 we prove a theorem of existence and uniqueness of a weak solution (u, P) of problem (1), (2). The proof is based on the Faedo-Galerkin method associated with a priori estimates, weak convergence and compactness techniques. In Part 3 we obtain an asymptotic expansion of the solution (u, P) of the problem (1), (2) up to order N+1 in three small parameters K, lambda, K1.
11
Content available remote Równania ewolucyjne z operatorem tłumienia
Winiarska T.
Czasopismo Techniczne. Mechanika
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2008
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R. 105, z. 4-M
143-154
PL
W artykule rozważa się problem ewolucyjny z operatorem tłumienia. Jest on ściśle związany z pewnym problemem z mechaniki. Występujące w tym zagadnieniu operatory powinny spełniać odpowiednie założenia i w zależności od tych założeń rozważa się cztery różne sytuacje. W każdej z nich podaje się twierdzenie o istnieniu i jednoznaczności rozwiązania.
EN
In the paper an evolution problem with a damping operator is considered. The issue is closely related to some problems of mechanics. Operators appearing in the problem should satisfy some conditions. Depending on these conditions four different cases are considered. In each of the cases a theorem on existence and uniqueness of solutions is presented.
12
Content available remote A note on a Herzog's and Lemmert's paper
Leszczyński H.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2005
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Vol. 45, [Z] 2
219--223
EN
We give an alternative view of the results published in the Herzog's and Lemmert's paper "On maximal and minimal solutions for x'(t)=F(t,x(t),x(h(t))), x(0)=x_0", Comment. Math. XL (2000), 93-102. One can observe that these results con be obtained by classical (elementary) methods, instead of tarski's fixed point theorems in partially ordered spaces.
13
Content available remote Dynamic Contact Problems With Slip-Dependent Friction in Viscoelasticity
Ionescu I. R., Nguyen Q. L.
International Journal of Applied Mathematics and Computer Science
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2002
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Vol. 12, no 1
71-80
EN
The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dimensional case.
14
Content available remote On some generalized Volterra condition and advanced argument for integral equations
Augustynowicz A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2000
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[Z] 40
7-17
EN
We study the existence and uniqueness problem for wide class of nonlinear integral functional equations with an unknown function of several variables. We assume that the right-hand side of the equation satisfies some generalization of the Volterra condition that, in some cases, admits an advanced argument at an unknown function. The result is illustrated for some Darboux problem.
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