Class Of Nonlinear Variational Inequalities Research Articles

Homogenization of a class of nonlinear variational inequalities with applications in fluid film flow

The authors consider the homogenization of a class of nonlinear variational inequalities, which include rapid oscillations with respect to a parameter. The homogenization of the corresponding class of differential equations is also studied. The results are applied to some models for the pressure in a thin fluid film fluid between two surfaces which are in relative motion. This is an important problem in the lubrication theory. In particular, the analysis includes the effects of surface roughness on both faces and the phenomenon of cavitation. Moreover, the fluid can be modeled as Newtonian or non-Newtonian by using a Rabinowitsch fluid model.

A general framework for the solvability of a class of nonlinear variational inequalities

A general framework for the solvability of a class of nonlinear variational inequalities

Nonlinear variational inequalities on reflexive Banach spaces andtopological vector spaces

The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented. The obtained results extend, improve, and unify the results due to Browder, Carbone, Siddiqi, Ansari, Kazmi, Verma, and others.

General auxiliary problem principle and solvability of a class of nonlinear mixed variational inequalities involving partially relaxed monotone mappings

The approximation–solvability of the following class of nonlinear variational inequality (NVI) problems based on a new general auxiliary problem principle is presented: Find an element x∗ ∈ K such that 〈 T(x∗), x − x∗〉 + f (x) − f (x∗) 0 for all x ∈ K, where T : K → H is a partially relaxed monotone mapping from a nonempty closed convex subset K of a real Hilbert space H into H , and f : K → R is a continuous convex function on K . The general auxiliary problem principle is described as follows: for given iterate xk ∈ K and for a constant ρ > 0 , determine xk+1 such that (for k 0 ) 〈 ρT(xk) + ρL(xk+1) + h′(xk+1) − ρL(xk) − h′(xk), x − xk+1〉 + ρ[f (x) − f (xk+1)] 0 for all x ∈ K , where L : K → H is any mapping on K , h : K → R is a function on K and h′ is the derivative of h . Mathematics subject classification (2000): 49J40.

A Combined Relaxation Method for a Class of Nonlinear Variational Inequalities

In this paper, we describe a class of combined relaxation methods for the non strictly monotone nonlinear variational inequality problem, which involves a max-type convex function. This method is readily implementable and attains a linear rate of convergence under certain additional assumptions.

Projection methods, algorithms, and a new system of nonlinear variational inequalities

The convergence of projection methods is based on a new iterative algorithm for the approximation-solvability of the following system of nonlinear variational inequalities (SNVI): determine elements x *, y * ϵ K such that 〈ϱ T( y *) + x * − y *, x − x *〉 ≥ 0, for all x ϵ K and for ϱ > 0, and 〈γ T( x *) + y * − x *, x − y *〉 ≥ 0, for all x ∈ K and for γ > 0, where T : K → H is a mapping from a nonempty closed convex subset K of a real Hilbert space H into H. This new class of generalized nonlinear variational inequalities reduces to standard class of nonlinear variational inequalities, which are widely studied and applied to various problems arising from mathematical sciences, optimization and control theory, and other related fields.

The solvability of a class of generalized nonlinear variational inequalities based on an iterative algorithm

Based on a new iterative algorithm, the solvability of a class of nonlinear variational inequalities involving a combination of relaxed monotone operators in a Hilbert space setting is presented.

A class of nonlinear variational inequalities involvingpseudomonotone operators

We present the solvability of a class of nonlinear variational inequalities involving pseudomonotone operators in a locally convex Hausdorff topological vector spaces setting. The obtained result generalizes similar variational inequality problems on monotone operators.

Solvability of generalized nonlinear symmetric variational inequalities

AbstractThis paper deals with the study of a general class of nonlinear variational inequalities. An existence result is given, and a perturbed iterative scheme is analyzed for solving such problems.

Variational inequalities in locally convex Hausdorff topological vector spaces

A class of nonlinear variational inequalities involving strongly G-monotone mappings in a locally convex Hausdorff topological vector space setting is presented. The obtained result generalizes the results on nonlinear variational inequalities on monotone and strongly monotone mappings.

A New Method for a Class of Nonlinear Set-valued Variational Inequalities

In this paper we construct a new iterative algorithm for solving a new class of nonlinear variational inequalities with set-valued mapping, and give some convergence analysis of iterative sequences generated by the algorithm.

Variational inequalities involving strongly pseudomonotone hemicontinuous mappings in nonreflexive Banach spaces

A new class of nonlinear variational inequalities involving strongly pseudomonotone hemicontinuous mappings is considered.

A new method for a class of nonlinear variational inequalities with fuzzy mappings

In this paper, we construct a new iterative algorithm of solution for a new class of nonlinear variational inequalities with fuzzy mappings and give some convergence analysis of iterative sequences generated by algorithm.

On interative algorithms for a class of nonlinear variational inequalities

In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.

An iterative algorithm for variational inequalities

In this paper, we introduce and study a new class of nonlinear variational inequalities. This new class enables us to apply variational techniques to the solution of differential equations of both odd and even orders. A projection method is used to suggest an iterative algorithm for finding the approximate solution of this class. We also discuss the convergence criteria of the proposed iterative algorithm. Several special cases are discussed, which can be obtained from the general result.

Finite element estimates for a class of nonlinear variational inequalities

It is well known that a wide class of obstacle and unilateral problems arising in pure and applied sciences can be studied in a general and unifield framework of variational inequalities. In this paper, we derive the error estimates for the finite element approximate solution for a class of highly nonlinear variational inequalities encountered in the field of elasticity and glaciology in terms ofW1,p(Ω)andLp(Ω)-norms. As a special case, we obtain the well-known error estimates for the corresponding linear obstacle problem and nonlinear problems.

On nonlinear variational inequalities

The fixed point technique is used to prove the existence of a solution for a class of nonlinear variational inequalities related with odd order constrained boundary value problems and to suggest an iterative algorithm to compute the approximate solution.

General nonlinear variational inequalities

The fixed point technique is used to prove the existence of a unique solution of a new unified and general class of nonlinear variational inequalities. Several special cases, which can be obtained from our main result, are also discussed.

Finite element analysis for a class of nonlinear variational inequalities

In this paper, we prove that the error estimates for the finite element approximation of a class of variational inequalities arising in elastostatics is of order h in the energy norm. In fact, our estimates improve all of the previously known error estimates for elliptic variational inequalities.

On some existence and uniqueness results in contact problems with nonlocal friction

THE WORKwe present is a mathematical study of Signorini's problem with friction: i.e. the problem of equilibrium of a linearly elastic body in contact with a rigid foundation. Until recently. the questions of existence and uniqueness of solutions to such problems were open. Recently. two ideas have appeared which have led to some positive results. The first. presented by Netas. Jarusek & Haslinger [11]. involves a concept of small friction and provides for the development of an existence result for a very special case of a uniformly loaded. infinite strip. The second. established by Duvaut [5]. is based on the idea of a nonlocal friction law which enables one to establish an existence result for 'any' friction and also to establish uniqueness for small friction. In this paper we present some new results in this direction and a new proof of a non local existence theory. Our approach differs considerably from the proof outlined in [5]. Instead of using fixed point arguments. we develop a theory of perturbed variational inequalities (the origin of which can be found in [9]) and establish a generalization for the class of nonlinear variational inequalities characterizing the non local Signorini problem. This approach should prove to be very useful in studies of approximations of friction prohlems.