Global Regularity And Uniqueness Of Solutions In A Surface Growth Model Using Rigorous A Posteriori Methods
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Global Regularity And Uniqueness Of Solutions In A Surface Growth Model Using Rigorous A Posteriori Methods
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Author : Christian Nolde
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2017
Global Regularity And Uniqueness Of Solutions In A Surface Growth Model Using Rigorous A Posteriori Methods written by Christian Nolde and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
The use of rigorous numerical methods to approach problems which can not be solved using standard methods (yet) has increased signifiantly in recent years. In this book, riogorous a-posteriori methods are used to study the time evolution of a surface growth model, given by a fourth order semi-linear parabolic partial differential equation, where standard methods fail to verify global uniqueness and smoothness of solutions. Based on an arbitrary numerical approximation, a-posteriori error-analysis is applied in order to prevent a blow up analytically. This is a method that in a similar way also applies to the three dimensional Navier-Stokes equations. The main idea consists of energy-estimates for the error between solution and approximation that yields a scalar differential equation controlling the norm of the error with coefficients depending solely on the numerical data. This allows the solution of the differential equation to be bounded using only numerical data. A key technical tool is a rigorous eigenvalue bound for the nonlinear operator linearized around the numerical approximation. The presented method succeeds to show global uniqueness for relatively large initial conditions, which is demonstrated in many numerical examples.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Chemical Sensors
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Author : Ghenadii Korotcenkov
language : en
Publisher: Momentum Press
Release Date : 2012-07-15
Chemical Sensors written by Ghenadii Korotcenkov and has been published by Momentum Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-15 with Technology & Engineering categories.
Chemical sensors are integral to the automation of myriad industrial processes and everyday monitoring of such activities as public safety, engine performance, medical therapeutics, and many more. This 4 volume reference work covering simulation and modeling will serve as the perfect complement to Momentum Press's 6 volume reference works 'Chemical Sensors: Fundamentals of Sensing Materials' and 'Chemical Sensors: Comprehensive Sensor Technologies', which present detailed information related to materials, technologies, construction and application of various devices for chemical sensing. This 4 volume comprehensive reference work analyzes approaches used for computer simulation and modeling in various fields of chemical sensing and discusses various phenomena important for chemical sensing such as bulk and surface diffusion, adsorption, surface reactions, sintering, conductivity, mass transport, interphase interactions, etc. In this work it will be shown that theoretical modeling and simulation of the processes, being a basic for chemical sensors operation, could provide considerable progress in choosing both optimal materials and optimal configurations of sensing elements for using in chemical sensors. Each simulation and modeling volume in the present series reviews modeling principles and approaches peculiar to specific groups of materials and devices applied for chemical sensing. Volume 2: Conductometric-Type Sensors covers phenomenological modeling and computational design of conductometric chemical sensors based on nanostructured materials such as metal oxides, carbon nanotubes and graphene. This volume contains an overview of the approaches used to quantitatively evaluate characteristics of sensitive structures in which electric charge transport depends on the interaction between the surfaces of the structures and chemical compounds in the surrounding.
Comprehensive Dissertation Index
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Author :
language : en
Publisher:
Release Date : 1989
Comprehensive Dissertation Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Dissertations, Academic categories.
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
The Finite Element Method Theory Implementation And Applications
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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
The Finite Element Method Theory Implementation And Applications written by Mats G. Larson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-13 with Computers categories.
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Geometric Level Set Methods In Imaging Vision And Graphics
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Author : Stanley Osher
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-17
Geometric Level Set Methods In Imaging Vision And Graphics written by Stanley Osher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-17 with Computers categories.
Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.
Computational Differential Equations
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Author : Kenneth Eriksson
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-05
Computational Differential Equations written by Kenneth Eriksson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-05 with Mathematics categories.
This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
A Course On Rough Paths
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Author : Peter K. Friz
language : en
Publisher: Springer Nature
Release Date : 2020-05-27
A Course On Rough Paths written by Peter K. Friz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-27 with Mathematics categories.
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Nonlocal Modeling Analysis And Computation
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Author : Qiang Du
language : en
Publisher: SIAM
Release Date : 2019-03-20
Nonlocal Modeling Analysis And Computation written by Qiang Du and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.