Well-Posed Nonlinear Problems
A Study of Mathematical Models of Contact
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54 Result(s)
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Mircea Sofonea
Mathematics
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Chapter
Inclusions
In this chapter we study the well-posedness of inclusions. We start with a stationary inclusion for which we prove the well-posedness with various Tykhonov triples, together with several convergence results, i...
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Chapter
Mathematical Modeling in Contact Mechanics
In this chapter, we present preliminary material needed in modeling and analysis of contact problems. This concerns the function spaces, the balance equations, the constitutive laws, and the interface laws. We...
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Chapter
Quasistatic Contact Problems
In this chapter, we study the well-posedness of several quasistatic mathematical models of contact. For each model, we introduce a classical formulation that gathers the corresponding equations, boundary, and ...
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Chapter
Nonlinear Problems and Their Classical Well-Posedness
We start this chapter with some preliminary material from functional analysis which will be used subsequently.
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Chapter
Fixed Point Problems
In this chapter, we deal with the well-posedness of fixed point problems of the form Λ u ...
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Chapter
Hemivariational Inequalities
In this chapter we present well-posedness results for hemivariational and variational–hemivariational inequalities in reflexive Banach spaces.
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Chapter
Minimization and Optimal Control Problems
We start this chapter with the well-posedness of a class of minimization problems. Thereby, under specific assumptions, we deduce their weak and strong generalized well-posedness in the sense of Hadamard. More...
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Chapter
Static Contact Problems
In this chapter, we study the well-posedness of several static mathematical models of contact. For each model, we introduce a classical formulation that gathers the corresponding equations and boundary conditi...
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Book
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Chapter
Tykhonov Triples and Associated Well-Posedness Concept
Inspired by the examples presented in Section
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Chapter
Variational Inequalities
In this chapter we present well-posedness results for variational inequalities.
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Article
Open AccessTykhonov well-posedness of fixed point problems in contact mechanics
We consider a fixed point problem S u = u ...
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Article
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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Article
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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Article
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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Article
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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Article
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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Article
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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Article
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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Article
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...
