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1
Content available remote 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
|
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
Content available Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent
Charkaoui Abderrahim, Fahim Houda, Alaa Nour Eddine
Opuscula Mathematica
|
2021
|
Vol. 41, no. 1
25--53
EN
We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent. Using Schaeffer’s fixed point theorem combined with the sub- and supersolution method, we prove the existence results of a weak solutions to the considered problems.
3
On strongly quasilinear elliptic systems with weak monotonicity
Azroul Elhoussine, Balaadich Farah
Journal of Applied Analysis
|
2021
|
Vol. 27, nr 1
153--162
EN
In this paper, we prove existence results in the setting of Sobolev spaces for a strongly quasilinear elliptic system by means of Young measures and mild monotonicity assumptions.
4
Content available A unique weak solution for a kind of coupled system of fractional Schrodinger equations
Abdolrazaghi Fatemeh, Razani Abdolrahman
Opuscula Mathematica
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2020
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Vol. 40, no. 3
313--322
EN
In this paper, we prove the existence of a unique weak solution for a class of fractional systems of Schrodinger equations by using the Minty-Browder theorem in the Cartesian space. To this aim, we need to impose some growth conditions to control the source functions with respect to dependent variables.
5
Content available Weak solutions of fractional order differential equations via Volterra-Stieltjes integral operator
El-Sayed A. M. A., El-Sayed W. G., Abd El-Mowla A. A. H.
Journal of Mathematics and Applications
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2017
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Vol. 40
85--96
EN
The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics ([18], [21]). In this paper, we study the existence of weak solutions for fractional differential equations of Riemann-Liouville and Caputo types. We depend on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type in reflexive Banach spaces.
6
Content available remote On the weak solutions of a coupled system of Volterra-Stieltjes integral equations
El-Sayed A. M. A., Al-Fadel M. M. A.
Commentationes Mathematicae
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2017
|
Vol 57, No. 2
143--151
EN
We present an existence theorem for at least one weak solution to a coupled system of Volterra-Stieltjes integral equations in a reflexive Banach space.
7
Content available Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces
Stancut I. L., Stircu I. D.
Opuscula Mathematica
|
2016
|
Vol. 36, no. 1
81--101
EN
In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential Von a bounded domain in Rn (N ≥ 3) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any λ > 0 is an eigenvalue of our problem. The second theorem states the existence of a constant [formula] such that any [formula] is an eigenvalue, while the third theorem claims the existence of a constant λ* > 0 such that every λ ∈ [λ*∞) is an eigenvalue of the problem.
8
Content available A Viscoelastic Frictionless Contact Problem with Adhesion
Touzaline A.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2015
|
Vol. 63, no. 1
53--66
EN
We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. The proof is based on arguments of evolution equations with multivalued maximal monotone operators, differential equations and the Banach fixed point theorem.
9
Content available remote The existence of a weak solution of the semilinear first-order differential equation in a Banach space
Jużyniec M.
Czasopismo Techniczne. Nauki Podstawowe
|
2014
|
R. 111, z. 2-NP
59--62
EN
This paper is devoted to the investigation of the existence and uniqueness of a suitably defined weak solution of the abstract semilinear value problem u'(t) = Au(t) + f(t, u(t)), u(0) = x with x ϵ X, where X is a Banach space. We are concerned with two types of solutions: weak and mild. Under the assumption that A is the generator of a strongly continuous semigroup of linear, bounded operators, we also establish sufficient conditions such that if u is a weak (mild) solution of the initial value problem, then u is a mild (weak) solution of that problem.
PL
Celem pracy jest przedstawienie twierdzenia o jednoznaczności i istnieniu słabego rozwiązania abstrakcyjnego semiliniowego równania różniczkowego u'(t) = Au(t) + f(t, u(t)), u(0) = x, gdzie x ϵ X, w przestrzeni Banacha X. W pracy rozważane są dwa typy rozwiązań: weak oraz mild. Przy założeniu, ze operator A jest generatorem silnie ciągłej półgrupy operatorów liniowych i ograniczonych, podane zostały również warunki wystarczające na to, aby rozwiązanie weak (mild) było rozwiązaniem mild (weak) tego zagadnienia.
10
Content available remote Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on RN
Anh C. T., Thuy L. T.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2013
|
Vol. 61, no 1
47--65
EN
We prove the existence of global attractors for the following semilinear degenerate parabolic equation on RN: ∂u/∂t−div(σ(x)∇u)+λu+f(x,u)=g(x), under a new condition concerning the variable nonnegative diffusivity σ(⋅) and for an arbitrary polynomial growth order of the nonlinearity f. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.
11
Content available remote Three Solutions Theorem for a Quasilinear Dirichlet Boundary Value Problem
Goncerz P.
Schedae Informaticae
|
2012
|
Vol. 21
159--168
EN
We consider a Dirichlet boundary value problem driven by the p-Laplacian with the right hand side being a Carathéodory function. The existence of solutions is obtained by the use of a special form of the three critical points theorem.
12
Content available Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces
Benchohra M., Mostefai F.
Opuscula Mathematica
|
2012
|
Vol. 32, no. 1
31-40
EN
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
13
Content available On the existence of three solutions for quasilinear elliptic problem
Goncerz P.
Opuscula Mathematica
|
2012
|
Vol. 32, no. 3
473-486
EN
We consider a quasilinear elliptic problem of the type - Δpu = λ (ƒ (u)+ μg(u)) in Ω, u/∂Ω = 0, where Ω ⊂ RN is an open and bounded set, ƒ, g are continuous real functions on R and , λ, μ ∈ R. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.
14
Content available On a class of nonhomogenous quasilinear problems in Orlicz-Sobolev spaces
Souayah A. K.
Opuscula Mathematica
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2012
|
Vol. 32, no. 4
731-750
EN
We study the nonlinear boundary value problem [formula], where Ω is a bounded domain in RN with smooth boundary, λ, μ are positive real numbers, q and α are continuous functions and a1,a2 are two mappings such that a1 (/t/)t; a2(/t/)t; are increasing homeomorphisms from R to R. The problem is analysed in the context of Orlicz-Soboev spaces. First we show the existence of infinitely many weak solutions for any λ, μ > 0. Second we prove that for any μ > 0, there exists λ* sufficiently small, and λ* large enough such that for any λ ∈ (0, λ*) ∪ (λ*, ∞), the above nonhomogeneous quasilinear problem has a non-trivial weak solution.
15
Content available remote On differentiability with respect to a parameter of a weak solution of a second order differential equation in Banach space
Jużyniec M.
Czasopismo Techniczne. Nauki Podstawowe
|
2010
|
R. 107, z. 1-NP
31-41
EN
The purpose of this paper is to present some theorems on continuity and differentiability with respect to a parameter h of a weak solution of the evolution equation u(t) = A[h]u(t) + f[h](t).
PL
Celem artykułu jest przedstawienie twierdzeń o ciągłej zależności od parametru oraz różniczkowalności względem parametru h słabego rozwiązania ewolucyjnego równania różniczkowego u(t) = A[h]u(t) + f[h](t).
16
Content available remote A dynamic prictionless contact problem with adhesion and damage
Selmani M., Selmani L.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2007
|
Vol. 55, no 1
17-34
EN
We consider a dynamic frictionless contact problem for a viscoelastic material with damage. The contact is modeled with normal compliance condition. The adhesion of the contact surfaces is considered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness of the solution. The proofs are based on the theory of evolution equations with monotone operators, a classical existence and uniqueness result for parabolic inequalities, and fixed point arguments.
17
An elastic contact problem with adhesion and normal compliance
Sofonea M., Matei A.
Journal of Applied Analysis
|
2006
|
Vol. 12, nr 1
19-36
EN
We study a mathematical problem describing the friction- less adhesive contact between an elastic body and a foundation. The adhesion process is modelled by a surface variable, the bonding field, and the contact is modelled with a normal compliance condition; the tangential shear due to the bonding field is included; the elastic consti- tutive law is assumed to be nonlinear and the process is quasistatic. The problem is formulated as a nonlinear system in which the unknowns are the displacement, the stress and the bonding field. The existence of a unique weak solution for the problem is established by using arguments for differential equations followed by the construction of an appropriate contraction mapping.
18
Existence for some quasilinear elliptic systems with critical growth nonlinearity and L 1 data
Alaa N., Maach F., Mounir I.
Journal of Applied Analysis
|
2005
|
Vol. 11, nr 1
81-94
EN
We prove the existence of weak solutions for some quasilinear elliptic reaction-diffusion systems with Dirichlet boundary conditions and satisfying to the two main properties: the positivity of the solutions and the balance law. The nonlinearity we consider here has critical growth with respect to the gradient and data are in L1.
19
Content available remote Asymptotic expansion of the solution for nonlinear wave equation with mixed non-homogeneous conditions
Long N. T., Dinh A. P. N., Diem T. N.
Demonstratio Mathematica
|
2003
|
Vol. 36, nr 3
683--695
20
A quasistatic contact problem with slip dependent coefficient of friction for elastic materials
Corneschi C., Hoarau-Mantel T.-V. T.-V., Sofonea M.
Journal of Applied Analysis
|
2002
|
Vol. 8, nr 1
63-82
EN
We consider a mathematical model which describes the frictional contact between a deformable body and an obstacle, say a foundation. The body is assumed to be linear elastic and the contact is modeled with a version of Coulomb's law of dry friction in which the normal stress is prescribed on the contact surface. The novelty consists here in the fact that we consider a slip dependent coefficient of friction and a quasistatic process. We present two alternative yet equivalent formulations of the problem and establish existence and uniqueness results. The proofs are based on a new result obtained in [10] in the study of evolutionary variational inequalities.
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