Well-Posed Nonlinear Problems
A Study of Mathematical Models of Contact
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31 Result(s)
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Mircea Sofonea
Solid Mechanics
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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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Book
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Chapter
A History-Dependent Variational-Hemivariational Inequality in Contact Mechanics
This chapter is closely related with Chap. 16 of this book. It deals with a mathematical model which describes the frictional contact between a viscoelastic body a...
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Chapter
A Variational-Hemivariational Inequality in Contact Mechanics
This chapter deals with a new mathematical model for the frictional contact between an elastic body and a rigid foundation covered by a deformable layer made of soft material. We study the model in the form of...
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Chapter
Modelling of Piezoelectric Contact Problems
We consider a mathematical model which describes the frictional contact between an electro-viscoelastic body and a conductive foundation. The process is dynamic and the contact is modelled with normal complian...
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Book
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Book
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Chapter
1 Introduction
Considerable progress has been achieved recently in modeling and mathematical analysis of various processes involved in contact between deformable bodies. Indeed, a general Mathematical Theory of Contact Mecha...
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Chapter
5 A Detailed Representative Problem
In the previous three chapters various constitutive laws for the behaviour of the material and different contact conditions were described in some detail. In this chapter we take the next step and assemble, in...
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Chapter
10 Slip or Temperature Dependent Frictional Contact
The frictional contact problems which have been described up to now contained a constant friction coefficient, although, as was described in Sect. 2.7, in many applications it depends on the slip speed, on the...
