43 Result(s)
within
Chapter
Mircea Sofonea
-
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...
-
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...
-
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 ...
-
Chapter
Nonlinear Problems and Their Classical Well-Posedness
We start this chapter with some preliminary material from functional analysis which will be used subsequently.
-
Chapter
Fixed Point Problems
In this chapter, we deal with the well-posedness of fixed point problems of the form Λ u ...
-
Chapter
Hemivariational Inequalities
In this chapter we present well-posedness results for hemivariational and variational–hemivariational inequalities in reflexive Banach spaces.
-
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...
-
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...
-
Chapter
Tykhonov Triples and Associated Well-Posedness Concept
Inspired by the examples presented in Section
-
Chapter
Variational Inequalities
In this chapter we present well-posedness results for variational inequalities.
-
Chapter
Optimal Control of Quasivariational Inequalities with Applications to Contact Mechanics
This chapter deals with the optimal control of a class of elliptic quasivariational inequalities. We start with an existence and uniqueness result for such inequalities. Then we state an optimal control proble...
-
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...
-
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...
-
Chapter and Conference Paper
A Multivalued Variational Inequality with Unilateral Constraints
The present paper represents a continuation of [3]. There, we studied a new class of variational inequalities involving a pseudomonotone univalued operator and a multivalued operator, for which we obtained an exi...
-
Chapter and Conference Paper
Variational Analysis of a Quasistatic Contact Problem
We start by proving an existence and uniqueness result for a new class of variational inequalities which arise in the study of quasistatic models of contact. The novelty lies in the special structure of these ...
-
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 ...
-
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...
-
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...
-
Chapter and Conference Paper
A Class of Mixed Variational Problems with Applications in Contact Mechanics
We provide an existence result in the study of a new class of mixed variational problems. The problems are formulated on unbounded interval of time and involve history-dependent operators. The proof is based o...
-
Chapter and Conference Paper
A Class of History-Dependent Inclusionswith Applications to Contact Problems
We consider a class of subdifferential inclusions which involve a history-dependent operator. We use arguments on pseudomonotone operators and fixed point in order to prove the unique solvability of such inclu...
