Nonlinear Pde S Dynamics And Continuum Physics
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Nonlinear Pde S Dynamics And Continuum Physics
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Author : J. L. Bona
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Nonlinear Pde S Dynamics And Continuum Physics written by J. L. Bona 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 2000 with Mathematics categories.
This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.
Quantization Pdes And Geometry
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Author : Dorothea Bahns
language : en
Publisher: Birkhäuser
Release Date : 2016-02-11
Quantization Pdes And Geometry written by Dorothea Bahns and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-11 with Mathematics categories.
This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.
Elliptic And Parabolic Problems
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Author : Catherine Bandle
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Elliptic And Parabolic Problems written by Catherine Bandle 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 2006-01-17 with Mathematics categories.
Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.
Fuchsian Reduction
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Author : Satyanad Kichenassamy
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-14
Fuchsian Reduction written by Satyanad Kichenassamy 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 2007-09-14 with Mathematics categories.
This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.
Laminations And Foliations In Dynamics Geometry And Topology
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Author : Mikhail Lyubich
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Laminations And Foliations In Dynamics Geometry And Topology written by Mikhail Lyubich 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 2001 with Mathematics categories.
This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference.
Hyperbolic Conservation Laws In Continuum Physics
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Author : Constantine M. Dafermos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Hyperbolic Conservation Laws In Continuum Physics written by Constantine M. Dafermos 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 2013-06-29 with Mathematics categories.
The seeds of Continuum Physics were planted with the works of the natural philosophers of the eighteenth century, most notably Euler; by the mid-nineteenth century, the trees were fully grown and ready to yield fruit. It was in this envi ronment that the study of gas dynamics gave birth to the theory of quasilinear hyperbolic systems in divergence form, commonly called "hyperbolic conserva tion laws"; and these two subjects have been traveling hand-in-hand over the past one hundred and fifty years. This book aims at presenting the theory of hyper bolic conservation laws from the standpoint of its genetic relation to Continuum Physics. Even though research is still marching at a brisk pace, both fields have attained by now the degree of maturity that would warrant the writing of such an exposition. In the realm of Continuum Physics, material bodies are realized as continuous media, and so-called "extensive quantities", such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws and constitutive equations. A self-contained, though skeletal, introduction to this branch of classical physics is presented in Chapter II. The reader may flesh it out with the help of a specialized text on the subject.
Nonlinear Dirac Equation Spectral Stability Of Solitary Waves
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Author : Nabile Boussaïd
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-11-21
Nonlinear Dirac Equation Spectral Stability Of Solitary Waves written by Nabile Boussaïd 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 2019-11-21 with Education categories.
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.
Differential Geometry And Continuum Mechanics
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Author : Gui-Qiang G. Chen
language : en
Publisher: Springer
Release Date : 2015-08-11
Differential Geometry And Continuum Mechanics written by Gui-Qiang G. Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-11 with Mathematics categories.
This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.
Singularities In Algebraic And Analytic Geometry
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Author : Caroline Grant Melles
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Singularities In Algebraic And Analytic Geometry written by Caroline Grant Melles 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 2000 with Mathematics categories.
This volume contains the proceedings of an AMS special session held at the 1999 Joint Mathematics Meetings in San Antonio. The participants were an international group of researchers studying singularities from algebraic and analytic viewpoints. The contributed papers contain original results as well as some expository and historical material. This volume is dedicated to Oscar Zariski, on the one hundredth anniversary of his birth. Topics include the role of valuation theory in algebraic geometry with recent applications to the structure of morphisms; algorithmic approaches to resolution of equisingular surface singularities and locally toric varieties; weak subintegral closures of ideals and Rees valuations; constructions of universal weakly subintegral extensions of rings; direct-sum decompositions of finitely generated modules; construction and examples of resolution graphs of surface singularities; Jacobians of meromorphic curves; investigation of spectral numbers of curve singularities using Puiseux pairs; Gröbner basis calculations of Hochschild homology for hypersurfaces with isolated singularities; and the theory of characteristic classes of singular spaces - a brief history with conjectures and open problems.
Instability Index Theorem And Exponential Trichotomy For Linear Hamiltonian Pdes
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Author : Zhiwu Lin
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-02
Instability Index Theorem And Exponential Trichotomy For Linear Hamiltonian Pdes written by Zhiwu Lin 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 2022-02-02 with Mathematics categories.
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