39 Result(s)
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Article
Mircea Sofonea
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Article
Convergence analysis for elliptic quasivariational inequalities
We deal with a class of elliptic quasivariational inequalities with constraints in a reflexive Banach space. We use arguments of monotonicity, convexity and compactness in order to prove a convergence criterio...
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Open AccessTykhonov well-posedness of fixed point problems in contact mechanics
We consider a fixed point problem S u = u ...
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Tykhonov well-posedness of a heat transfer problem with unilateral constraints
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain D ⊂ ℝd and its weak formulation is in the fo...
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Open AccessHistory-dependent operators and prox-regular swee** processes
We consider an abstract inclusion in a real Hilbert space, governed by an almost history-dependent operator and a time-dependent multimap** with prox-regular values. We establish the unique solvability of th...
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A generalized penalty method for differential variational-hemivariational inequalities
We consider a differential variational-hemivariational inequality with constraints, in the framework of reflexive Banach spaces. The existence of a unique mild solution of the inequality, together with its sta...
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Minimization arguments in analysis of variational–hemivariational inequalities
In this paper, an alternative approach is provided in the well-posedness analysis of elliptic variational–hemivariational inequalities in real Hilbert spaces. This includes the unique solvability and continuou...
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Generalized Penalty Method for Elliptic Variational–Hemivariational Inequalities
We consider an elliptic variational–hemivariational inequality with constraints in a reflexive Banach space, denoted \(\mathcal{P}\) ...
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Well-Posedness of Minimization Problems in Contact Mechanics
We consider an abstract minimization problem in reflexive Banach spaces together with a specific family of approximating sets, constructed by perturbing the cost functional and the set of constraints. For this...
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A Class of Nonlinear Inclusions and Swee** Processes in Solid Mechanics
We consider a new class of inclusions in Hilbert spaces for which we provide an existence and uniqueness result. The proof is based on arguments of monotonicity, convexity and fixed point. We use this result t...
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Convergence and Optimization Results for a History-Dependent Variational Problem
We consider a mixed variational problem in real Hilbert spaces, defined on the unbounded interval of time [ ...
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On the Tykhonov Well-Posedness of an Antiplane Shear Problem
We consider a boundary value problem which describes the frictional antiplane shear of an elastic body. The process is static and friction is modeled with a slip-dependent version of Coulomb’s law of dry frict...
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A Tykhonov-type well-posedness concept for elliptic hemivariational inequalities
In this paper, we introduce a new Tykhonov-type well-posedness concept for elliptic hemivariational inequalities, governed by an approximating function h. We characterize the well-posedness in terms of the metric...
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Open AccessTykhonov well-posedness of split problems
In (J. Optim. Theory Appl. 183:139–157, 2019) we introduced and studied the concept of well-posedness in the sense of Tykhonov for abstract problems formulated on metric spaces. Our aim of this current paper is t...
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On the Well-Posedness Concept in the Sense of Tykhonov
We introduce a general concept of well-posedness in the sense of Tykhonov for abstract problems formulated on metric spaces and characterize it in terms of properties for a family of approximating sets. Then, ...
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Convergence analysis of penalty based numerical methods for constrained inequality problems
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variation...
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Optimal control for a class of mixed variational problems
The present paper concerns a class of abstract mixed variational problems governed by a strongly monotone Lipschitz continuous operator. With the existence and uniqueness results in the literature for the prob...
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Optimal Control of a Class of Variational–Hemivariational Inequalities in Reflexive Banach Spaces
The present paper represents a continuation of Migórski et al. (J Elast 127:151–178, 2017). There, the analysis of a new class of elliptic variational–hemivariational inequalities in reflexive Banach spaces, incl...
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Time-dependent inclusions and swee** processes in contact mechanics
We consider a class of time-dependent inclusions in Hilbert spaces for which we state and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities, convex analysis ...
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History-Dependent Inequalities for Contact Problems with Locking Materials
We consider a class of history-dependent variational–hemivariational inequalities with constraints. Besides the unique solvability of the inequalities, we study the behavior of the solution with respect to the...
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Optimization problems for elastic contact models with unilateral constraints
The aim of this paper is to provide some results in the study of an abstract optimization problem in reflexive Banach spaces and to illustrate their use in the analysis and control of static contact problems w...
