Linear And Nonlinear Perturbations Of The Operator Operatorname Div
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Black Holes In Higher Dimensions
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Author : Gary T. Horowitz
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-19
Black Holes In Higher Dimensions written by Gary T. Horowitz 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 2012-04-19 with Science categories.
The first book devoted to black holes in more than four dimensions, for graduate students and researchers.
Hemivariational Inequalities
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Author : Panagiotis D. Panagiotopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hemivariational Inequalities written by Panagiotis D. Panagiotopoulos 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 2012-12-06 with Technology & Engineering categories.
The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.
A First Course In Sobolev Spaces
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Author : Giovanni Leoni
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
A First Course In Sobolev Spaces written by Giovanni Leoni and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-17 with Mathematics categories.
This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.
Linear And Nonlinear Perturbations Of The Operator Div
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Author : Viktor Grigorʹevich Osmolovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Linear And Nonlinear Perturbations Of The Operator Div written by Viktor Grigorʹevich Osmolovskiĭ and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation $F(\dot y,y,x)=0$. Taking as linearization the first order operator $Lu=C_{ij}u_{x_j}^i+C_iu^i$, one can, under certain conditions, regard the operator $L$ as a compact perturbation of the operator div. This book presents results on boundary-value problems for $L$ and the theory of nonlinear perturbations of $L$. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator $L$. An analog of the Weyl decomposition is proved. The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ for which $L$ is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ is given. The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.
Mathematics Of Wave Phenomena
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Author : Willy Dörfler
language : en
Publisher: Springer Nature
Release Date : 2020-10-01
Mathematics Of Wave Phenomena written by Willy Dörfler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.
Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.
Sobolev Spaces On Riemannian Manifolds
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Author : Emmanuel Hebey
language : en
Publisher: Springer
Release Date : 2006-11-14
Sobolev Spaces On Riemannian Manifolds written by Emmanuel Hebey and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey's presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be weakened, and also presents new results.
Mean Field Games
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Author : Yves Achdou
language : en
Publisher: Springer Nature
Release Date : 2021-01-19
Mean Field Games written by Yves Achdou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-19 with Mathematics categories.
This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.
Linear And Nonlinear Perturbations Of The Operator Operatorname Div
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Author : Viktor Grigorʹevich Osmolovskiĭ
language : en
Publisher:
Release Date : 1997
Linear And Nonlinear Perturbations Of The Operator Operatorname Div written by Viktor Grigorʹevich Osmolovskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Boundary value problems categories.
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation F(\dot y, y, x)=0. Taking as linearization the first order operator Lu=C_{ij}u_{x_j}^i+C_iu^i, one can, under certain conditions, regard the operator L as a compact perturbation of the operator div. This book presents results on boundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. An a.
The Physics Of Nuclear Reactors
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Author : Serge Marguet
language : en
Publisher: Springer
Release Date : 2018-02-26
The Physics Of Nuclear Reactors written by Serge Marguet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-26 with Science categories.
This comprehensive volume offers readers a progressive and highly detailed introduction to the complex behavior of neutrons in general, and in the context of nuclear power generation. A compendium and handbook for nuclear engineers, a source of teaching material for academic lecturers as well as a graduate text for advanced students and other non-experts wishing to enter this field, it is based on the author’s teaching and research experience and his recognized expertise in nuclear safety. After recapping a number of points in nuclear physics, placing the theoretical notions in their historical context, the book successively reveals the latest quantitative theories concerning: • The slowing-down of neutrons in matter • The charged particles and electromagnetic rays • The calculation scheme, especially the simplification hypothesis • The concept of criticality based on chain reactions • The theory of homogeneous and heterogeneous reactors • The problem of self-shielding • The theory of the nuclear reflector, a subject largely ignored in literature • The computational methods in transport and diffusion theories Complemented by more than 400 bibliographical references, some of which are commented and annotated, and augmented by an appendix on the history of reactor physics at EDF (Electricité De France), this book is the most comprehensive and up-to-date introduction to and reference resource in neutronics and reactor theory.
Positive Operator Semigroups
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Author : András Bátkai
language : en
Publisher: Birkhäuser
Release Date : 2017-02-13
Positive Operator Semigroups written by András Bátkai and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-13 with Mathematics categories.
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.