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It describes phenomena which are modelled by partial differential equations. Applied Partial Differential Equations:: A Visual Approach th Edition.
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They include flows of fluids and gases, granular-material flows, biological processes such as pattern formation on animal skins, kinetics of rarified gases, free boundaries, semiconductor devices, and socioeconomic processes. Each topic is briefly introduced in its scientific or engineering context, followed by a presentation of the mathematical models in the form of partial differential equations with a discussion of their basic mathematical properties.
The author illustrates each chapter by a series of his own high-quality photographs, which demonstrate that partial differential equations are powerful tools for modeling a large variety of phenomena influencing our daily lives. In this book the static semiconductor device problem is presented and analysed from an applied mathematician's point of view.
To me personally the most fascinating aspect of mathematical device analysis is that an interplay of abstract mathematics, perturbation theory, numerical analysis and device physics is prompting the design and development of new technology. I very much hope to convey to the reader the importance of applied mathematics for technological progress.
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Each chapter of this book is designed to be as selfcontained as possible, however, the mathematical analysis of the device problem requires tools which cannot be presented completely here. Also, at the beginning of each chapter I refer to textbooks which introduce the interested reader to the required mathematical concepts. Semiconductor equations by Peter A Markowich Book 21 editions published between and in English and Undetermined and held by WorldCat member libraries worldwide This book contains the first unified account of the currently used mathematical models for charge transport in semiconductor devices.
It is focussed on a presentation of a hierarchy of models ranging from kinetic quantum transport equations to the classical drift diffusion equations.
Particular emphasis is given to the derivation of the models, an analysis of the solution structure, and an explanation of the most important devices. The relations between the different models and the physical assumptions needed for their respective validity are clarified. The book addresses applied mathematicians, electrical engineers and solid-state physicists. It is accessible to graduate students in each of the three fields, since mathematical details are replaced by references to the literature to a large extent. It provides a reference text for researchers in the field as well as a text for graduate courses and seminars.
Mathematical problems in semiconductor physics Book 7 editions published in in English and held by WorldCat member libraries worldwide. Modeling of collisions by A Decoster Book 6 editions published between and in English and held by 79 WorldCat member libraries worldwide. They represent a cross-section of the research field Applied Nonlinear Analysis with emphasis on free boundaries, fully nonlinear partial differential equations, variational methods, quasilinear partial differential equations and nonlinear kinetic models.
Nonequilibrium problems in many-particle systems : lectures given at the 3rd Session of the Centro internazionale matematico estivo C. Decay to equilibrium for energy-reaction-diffusion systems by Jan Haskovec 1 edition published in in English and held by 8 WorldCat member libraries worldwide We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation.
While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow.
The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer thermodynamical equilibrium given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential.
Applied Partial Differential Equations: A Visual Approach
A theory for the approximation of solutions of boundary value problems on infinite intervals by Peter A Markowich Book 5 editions published in in English and Undetermined and held by 8 WorldCat member libraries worldwide An ad hoc method to solve boundary value problems which are posed on infinite intervals is to reduce the infinite interval to a finite but large one and to impose additional boundary conditions at the far end.
These boundary conditions should be posed in a way so that they express the asymptotic behaviour of the actual solution well.
In this paper a rigorous theory is derived which defines classes of appropriate additional boundary conditions. Appropriate is to be understood in the sense that the solutions of the approximate problems converge to the actual solution of the 'infinite' problem as the length of the finite interval tends to infinity. Moreover boundary conditions which produce convergence with the largest expectable order are devised. Check out his page for errata. Jost J. Partial Differential Equations King A.
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Otto S. Notes for Partial Differential Equations [. Markowich P. Sattinger D. Partial Differential Equations of Applied Mathematics [.
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