An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions

We consider a Cauchy problem for the Laplace equation in a two-dimensional semi-infinite region with a bounded inclusion, i.e. the region is the intersection between a half-plane and the exterior of a bounded closed curve contained in the half-plane. The Cauchy data are given on the unbounded part of the boundary of the region and the aim is to construct the solution on the boundary of the inclusion. In 1989, Kozlov and Maz'ya [10] proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems in bounded domains. We extend their approach to our setting and in each iteration step mixed boundary value problems for the Laplace equation in the semi-infinite region are solved. Well-posedness of these mixed problems are investigated and convergence of the alternating procedure is examined. For the numerical implementation an efficient boundary integral equation method is proposed, based on the indirect variant of the boundary integral equation approach. The mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing the feasibility of the proposed method.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

New methods for movement technique development in cross-country skiing using mathematical models and simulation

This Licentiate Thesis is devoted to the presentation and discussion of some new contributions in applied mathematics directed towards scientific computing in sports engineering. It considers inverse problems of biomechanical simulations with rigid body musculoskeletal systems especially in cross-country skiing. This is a contrast to the main research on cross-country skiing biomechanics, which is based mainly on experimental testing alone. The thesis consists of an introduction and five papers. The introduction motivates the context of the papers and puts them into a more general framework. Two papers (D and E) consider studies of real questions in cross-country skiing, which are modelled and simulated. The results give some interesting indications, concerning these challenging questions, which can be used as a basis for further research. However, the measurements are not accurate enough to give the final answers. Paper C is a simulation study which is more extensive than paper D and E, and is compared to electromyography measurements in the literature. Validation in biomechanical simulations is difficult and reducing mathematical errors is one way of reaching closer to more realistic results. Paper A examines well-posedness for forward dynamics with full muscle dynamics. Moreover, paper B is a technical report which describes the problem formulation and mathematical models and simulation from paper A in more detail. Our new modelling together with the simulations enable new possibilities. This is similar to simulations of applications in other engineering fields, and need in the same way be handled with care in order to achieve reliable results. The results in this thesis indicate that it can be very useful to use mathematical modelling and numerical simulations when describing cross-country skiing biomechanics. Hence, this thesis contributes to the possibility of beginning to use and develop such modelling and simulation techniques also in this context.

Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

Global migration : patriarchy, propoganda and the well- being of women and children

This critical analysis explores the conflicted position of women as ''trailing spouses" and the effects on families who relocate globally under the auspices of a multinational corporation, by utilizing a discursive analysis of two contemporary films and available literature. Current portrayals of women and children in contemporary media provide emotional yet conflicting images of the perfect woman, wife, mother, child and family. The basic tenets of a North American patriarchal economic system are being televised around the world. Technological advancements have made it possible to advertise political agendas on a global television screen. Much of what we see is propaganda couched in films and advertisements that are designed to romantic~e the practice of deriving profits from the unpaid labor of woman and invisibility of children and child rearing. I intend to show that the materiality of trailing a spouse globally conflicts with these romanticized images and supports feminist literature that asserts the notion that mothers and children are oppressed and managed for the benefit of capital.

Well-Being Freedom and The Possibility of Public-Provision Unit in Global Context

The purpose of this paper is, first, to investigate the interconnections of substantive freedoms, which are indispensable for every individual to “lead the kind of lives they have reason to value” (Sen, 1999b, p.10,18), and which have legitimate and ethical reasons to be publicly secured, second, to investigate a conception of public-provision unit that embodies “the right to well-being freedom”, and a conception of decision-making unit that corresponds to it, based on the perspective of Sen’s capability theory and its extension, comparing with that of Rawls’ Theory of Justice and A Law of People. If we intend to construct such a public-provision unit, which conducts redistribution as a whole, and which receives every individual who cannot belong to any fixed local group, what kind of a body should we assume as a public-provision unit? And further, what kind of a body should we assume as a decision-making unit, which is responsible for deciding or revising the basic conceptions of public provision unit?

Moral Loopholes in the Global Economic Environment: Why Well-Intentioned Organizations Act in Harmful Ways

Thomas Pogge’s notion of moral loopholes serves to provide support for two claims: first, that the ethical code of the global economic order contains moral loopholes that allow participants in special social arrangements to reduce their obligations to those outside the social arrangement, which leads to morally objectionable actions for which no party feels responsible and that are also counterproductive to the overall objective of the economic system; and, second, that these moral loopholes are more likely to exist as our economic order becomes more global. Finally, it will be shown that attempts to rectify the situation with voluntary corporate codes of conduct are inadequate. The argument proceeds through analysis of one case study, concerning action by the executive of the Cerrejón mining operation at La Guajira Penisular, Colombia.

Moral Loopholes in the Global Economic Environment: Why Well-Intentioned Organizations Act in Harmful Ways

Thomas Pogge’s notion of moral loopholes serves to provide support for two claims: first, that the ethical code of the global economic order contains moral loopholes that allow participants in special social arrangements to reduce their obligations to those outside the social arrangement, which leads to morally objectionable actions for which no party feels responsible and that are also counterproductive to the overall objective of the economic system; and, second, that these moral loopholes are more likely to exist as our economic order becomes more global. Finally, it will be shown that attempts to rectify the situation with voluntary corporate codes of conduct are inadequate. The argument proceeds through analysis of one case study, concerning action by the executive of the Cerrejón mining operation at La Guajira Penisular, Colombia.

Moral Loopholes in the Global Economic Environment: Why Well-Intentioned Organizations Act in Harmful Ways

Thomas Pogge’s notion of moral loopholes serves to provide support for two claims: first, that the ethical code of the global economic order contains moral loopholes that allow participants in special social arrangements to reduce their obligations to those outside the social arrangement, which leads to morally objectionable actions for which no party feels responsible and that are also counterproductive to the overall objective of the economic system; and, second, that these moral loopholes are more likely to exist as our economic order becomes more global. Finally, it will be shown that attempts to rectify the situation with voluntary corporate codes of conduct are inadequate. The argument proceeds through analysis of one case study, concerning action by the executive of the Cerrejón mining operation at La Guajira Penisular, Colombia.

How well can we simulate past climates? Evaluating the models using global palaeoenvironmental datasets.

Global syntheses of palaeoenvironmental data are required to test climate models under conditions different from the present. Data sets for this purpose contain data from spatially extensive networks of sites. The data are either directly comparable to model output or readily interpretable in terms of modelled climate variables. Data sets must contain sufficient documentation to distinguish between raw (primary) and interpreted (secondary, tertiary) data, to evaluate the assumptions involved in interpretation of the data, to exercise quality control, and to select data appropriate for specific goals. Four data bases for the Late Quaternary, documenting changes in lake levels since 30 kyr BP (the Global Lake Status Data Base), vegetation distribution at 18 kyr and 6 kyr BP (BIOME 6000), aeolian accumulation rates during the last glacial-interglacial cycle (DIRTMAP), and tropical terrestrial climates at the Last Glacial Maximum (the LGM Tropical Terrestrial Data Synthesis) are summarised. Each has been used to evaluate simulations of Last Glacial Maximum (LGM: 21 calendar kyr BP) and/or mid-Holocene (6 cal. kyr BP) environments. Comparisons have demonstrated that changes in radiative forcing and orography due to orbital and ice-sheet variations explain the first-order, broad-scale (in space and time) features of global climate change since the LGM. However, atmospheric models forced by 6 cal. kyr BP orbital changes with unchanged surface conditions fail to capture quantitative aspects of the observed climate, including the greatly increased magnitude and northward shift of the African monsoon during the early to mid-Holocene. Similarly, comparisons with palaeoenvironmental datasets show that atmospheric models have underestimated the magnitude of cooling and drying of much of the land surface at the LGM. The inclusion of feedbacks due to changes in ocean- and land-surface conditions at both times, and atmospheric dust loading at the LGM, appears to be required in order to produce a better simulation of these past climates. The development of Earth system models incorporating the dynamic interactions among ocean, atmosphere, and vegetation is therefore mandated by Quaternary science results as well as climatological principles. For greatest scientific benefit, this development must be paralleled by continued advances in palaeodata analysis and synthesis, which in turn will help to define questions that call for new focused data collection efforts.