Well-Posedness by Perturbations for Variational-Hemivariational Inequalities

We generalize the concept of well-posedness by perturbations for optimization problem to a class of variational-hemivariational inequalities. We establish some metric characterizations of the well-posedness by perturbations for the variational-hemivariational inequality and prove their equivalence between the well-posedness by perturbations for the variational-hemivariational inequality and the well-posedness by perturbations for the corresponding inclusion problem

Stability analysis of partial differential variational inequalities in Banach spaces

In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques

Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities

In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hemivariational inequalities involving history-dependent operators and related problems with periodic and antiperiodic boundary conditions. The applicability of our theoretical results is illustrated through applications to a fractional evolution inclusion and a dynamic semipermeability problem

Advances in Multiscale and Multifield Solid Material Interfaces

Interfaces play an essential role in determining the mechanical properties and the structural integrity of a wide variety of technological materials. As new manufacturing methods become available, interface engineering and architecture at multiscale length levels in multi-physics materials open up to applications with high innovation potential. This Special Issue is dedicated to recent advances in fundamental and applications of solid material interfaces

Well-Posedness for a Class of Strongly Mixed Variational-Hemivariational Inequalities with Perturbations

The concept of well-posedness for a minimization problem is extended to develop the concept of well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations which includes as a special case the class of variational-hemivariational inequalities with perturbations. We establish some metric characterizations for the well-posed strongly mixed variational-hemivariational inequality and give some conditions under which the strongly mixed variational-hemivariational inequality is strongly well-posed in the generalized sense. On the other hand, it is also proven that under some mild conditions there holds the equivalence between the well posedness for a strongly mixed variational-hemivariational inequality and the well-posedness for the corresponding inclusion problem

Full Stability In Optimization

The dissertation concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to parametric variational systems including the well-known generalized equations and variational inequalities. Many relationships of full stability with the conventional notions of strong regularity and strong stability are established for a large class of problems of constrained optimization with twice continuously differentiable data. Other applications of full stability to nonlinear programming, to semidefinite programming, and to optimal control problems governed by semilinear elliptic PDEs are also studied

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin

Viscous contact problems in glaciology

Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. They can be modelled by coupling the Stokes equations with contact boundary conditions and a free boundary equation that evolves the geometry of the domain occupied by the fluid. These problems are of particular importance in glaciology, where they arise in the study of grounding lines and subglacial cavities. This work investigates the numerical approximation of viscous contact problems with applications to these two examples in glaciology. We commence by formulating the viscous contact problems that model subglacial cavitation and marine ice sheets in Chapter 1. We state the different variational inequalities that arise in these problems and are equivalent to the Stokes equations with contact boundary conditions. We then propose a novel framework for building numerical schemes for these problems in Chapter 2. This framework considers a family of discrete variational inequalities and establishes certain conditions that should be satisfied when approximating the free boundary equations. We then describe the numerical scheme that is used for the remainder of this work and compare it with different schemes that fit the framework introduced beforehand. Chapter 3 is dedicated to the numerical analysis of one of the Stokes variational inequalities formulated in this work. We give rigorous proofs on the conditions under which it is well-posed and its finite element approximation converges. By developing theoretical tools based on existing work in the numerical analysis of variational inequalities and p-Stokes systems, our analysis deals with three substantial difficulties arising in this system: the presence of rigid modes in the space of admissible velocity fields, the nonlinear rheology used in glaciology, and the friction boundary condition enforced at the base of glaciers. Chapter 4 presents a numerical investigation of subglacial cavitation and its application to glacial sliding under steady and unsteady conditions. We reconstruct steady friction laws by calculating several steady cavity shapes. These steady results are validated by comparing them to a linearised analytical method. We then perturb some of these steady states with oscillating water pressures that reveal an interplay between the frequency of the perturbations and the resulting sliding speed and cavity volume. Moreover, we find that if the steady state is located on the downsloping or rate-weakening part of the friction law, the cavity evolves towards the upsloping section, indicating that the downsloping part is unstable. Finally, we explore steady marine ice sheet configurations in Chapter 4. We do so by computing steady states to the parallel slab marine ice sheet problem, which we propose in this chapter. In this problem, a slab of ice of uniform thickness flows down an inclined bedrock into the ocean. We enforce influx conditions that allow us to explore a spectrum of flow regimes, ranging from sliding to shear-dominated flow. We find that the flux-thickness relationship at the grounding line takes the form of power laws with exponents n+1 and n+2 in these two limits, respectively, where n is a non-dimensional parameter in Glen's law, the power law rheology used commonly used in glaciology. We derive analytical approximations in these limits which resemble our numerical findings closely, with visible deviations in some cases. Our numerical results allow us to understand the shortcomings of these commonly used analytical methods. Moreover, in the context of the parallel slab problem, we find that the flux-thickness relationships are strictly monotonically increasing and that the bedrock plays a prominent role in the sliding dominated regime

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