Constrained variational-hemivariationalinequalities on nonconvex star-shaped sets

In this paper, we study a class of constrained variational–hemivariational inequality problems with nonconvex sets which are star-shaped with respect to a certain ball in a reflexive Banach space. The inequality is a fully nonconvex counterpart of the variational–hemivariational inequality of elliptic type since it contains both, a convex potential and a locally Lipschitz one. Two new results on the existence of a solution are proved by a penalty method applied to a variational–hemivariational inequality penalized by the generalized directional derivative of the distance function of the constraint set. In the first existence theorem, the strong monotonicity of the governing operator and a relaxed monotonicity condition of the Clarke subgradient are assumed. In the second existence result, these two hypotheses are relaxed and a suitable hypothesis on the upper semicontinuity of the operator is adopted. In both results, the penalized problems are solved by using the Knaster, Kuratowski, and Mazurkiewicz (KKM) lemma. For a suffciently small penalty parameter, the solution to the penalized problem solves also the original one. Finally, we work out an example on the interior and boundary semipermeability problem that ilustrate the applicability of our results

Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.Comment: 22 page

Convergence of simultaneous distributed-boundary parabolic optimal control problems

We consider a heat conduction problem S with mixed boundary conditions in a n-dimensional domain Ω with regular boundary Γ and a family of problems Sα, where the parameter α > 0 is the heat transfer coefficient on the portion of the boundary Γ1 . In relation to these state systems, we formulate simultaneous distributed-boundary optimal control problems on the internal energy g and the heat flux q on the complementary portion of the boundary Γ2 . We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system and the adjoint states when the heat transfer coefficient α goes to infinity. Finally, we prove estimations between the simultaneous distributed-boundary optimal control and the distributed optimal control problem studied in a previous paper of the first author.Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral; ArgentinaFil: Bollo, Carolina María. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; ArgentinaFil: Gariboldi, Claudia Maricel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; Argentin

Advances in Optimization and Nonlinear Analysis

The present book focuses on that part of calculus of variations, optimization, nonlinear analysis and related applications which combines tools and methods from partial differential equations with geometrical techniques. More precisely, this work is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The book is a valuable guide for researchers, engineers and students in the field of mathematics, operations research, optimal control science, artificial intelligence, management science and economics

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described