Well-Posed Nonlinear Problems
A Study of Mathematical Models of Contact
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Mircea Sofonea
Mathematical Modeling and Industrial 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
Numerical solution of a contact problem with unilateral constraint and history-dependent penetration
A numerical method is presented for a mathematical model which describes the frictionless contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic, and the cont...
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Book
Advances in Variational and Hemivariational Inequalities
Theory, Numerical Analysis, and Applications
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Chapter
A Hyperelastic Dynamic Frictional Contact Model with Energy-Consistent Properties
In this chapter we present an energy-consistent numerical model for the dynamic frictional contact between a hyperlastic body and a foundation. Our contribution has two traits of novelty. The first one arises ...
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Chapter
Two History-Dependent Contact Problems
We consider two initial boundary value problems which describe the evolution of a viscoelastic and viscoplastic body, respectively, in contact with a piston or a device. In both problems the contact process is...
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Chapter
Evolutionary Inclusions and Hemivariational Inequalities
We consider a class of abstract nonlinear evolutionary inclusions of first order with a multivalued Clarke subgradient term. We use a surjectivity result for pseudomonotone multivalued operators in order to pr...
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Book
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Chapter
Preliminaries
In this chapter we present preliminary material from functional analysis which will be used subsequently. The results are stated without proofs, since they are standard and can be found in many references. For...
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Chapter
Elements of Nonlinear Analysis
In this chapter we present basic material on the set-valued map**s, nonsmooth analysis, subdifferential calculus, and operators of monotone type. For set-valued map**s we concentrate on measurability and c...
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Chapter
Evolutionary Inclusions and Hemivariational Inequalities
In this chapter we study evolutionary inclusions of second order. These are multivalued relations which involve the second-order time derivative of the unknown. We start with a basic existence result for such ...
