Well-Posed Nonlinear Problems
A Study of Mathematical Models of Contact
Article
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...
Chapter
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
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
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
We start this chapter with some preliminary material from functional analysis which will be used subsequently.
Chapter
In this chapter, we deal with the well-posedness of fixed point problems of the form Λ u ...
Chapter
In this chapter we present well-posedness results for hemivariational and variational–hemivariational inequalities in reflexive Banach spaces.
Chapter
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
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...
Book
Chapter
Inspired by the examples presented in Section
Chapter
In this chapter we present well-posedness results for variational inequalities.
Article
We consider a fixed point problem S u = u ...
Article
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...
Article
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...
Article
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...
Article
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...
Article
We consider an elliptic variational–hemivariational inequality with constraints in a reflexive Banach space, denoted \(\mathcal{P}\) ...
Article
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...
Article
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...