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Geometric Analysis Of Hyperbolic Differential Equations
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Book Synopsis Geometric Analysis of Hyperbolic Differential Equations: An Introduction by : S. Alinhac
Download or read book Geometric Analysis of Hyperbolic Differential Equations: An Introduction written by S. Alinhac and published by Cambridge University Press. This book was released on 2010-05-20 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.
Book Synopsis Geometric Analysis of Hyperbolic Differential Equations by : Serge Alinhac
Download or read book Geometric Analysis of Hyperbolic Differential Equations written by Serge Alinhac and published by . This book was released on 2010 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required"--Provided by publisher.
Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Stefan Hildebrandt
Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Stefan Hildebrandt and published by Springer Science & Business Media. This book was released on 2003 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.
Book Synopsis Hyperbolic Partial Differential Equations and Geometric Optics by : Jeffrey Rauch
Download or read book Hyperbolic Partial Differential Equations and Geometric Optics written by Jeffrey Rauch and published by American Mathematical Soc.. This book was released on 2012-05-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.
Book Synopsis Elliptic–Hyperbolic Partial Differential Equations by : Thomas H. Otway
Download or read book Elliptic–Hyperbolic Partial Differential Equations written by Thomas H. Otway and published by Springer. This book was released on 2015-07-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
Book Synopsis Hyperbolic Problems and Regularity Questions by : Mariarosaria Padula
Download or read book Hyperbolic Problems and Regularity Questions written by Mariarosaria Padula and published by Springer Science & Business Media. This book was released on 2007-01-21 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
Book Synopsis Hyperbolic Partial Differential Equations and Wave Phenomena by : Mitsuru Ikawa
Download or read book Hyperbolic Partial Differential Equations and Wave Phenomena written by Mitsuru Ikawa and published by American Mathematical Soc.. This book was released on 2000 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The familiar wave equation is the most fundamental hyperbolic partial differential equation. Other hyperbolic equations, both linear and nonlinear, exhibit many wave-like phenomena. The primary theme of this book is the mathematical investigation of such wave phenomena. The exposition begins with derivations of some wave equations, including waves in an elastic body, such as those observed in connection with earthquakes. Certain existence results are proved early on, allowing the later analysis to concentrate on properties of solutions. The existence of solutions is established using methods from functional analysis. Many of the properties are developed using methods of asymptotic solutions. The last chapter contains an analysis of the decay of the local energy of solutions. This analysis shows, in particular, that in a connected exterior domain, disturbances gradually drift into the distance and the effect of a disturbance in a bounded domain becomes small after sufficient time passes. The book is geared toward a wide audience interested in PDEs. Prerequisite to the text are some real analysis and elementary functional analysis. It would be suitable for use as a text in PDEs or mathematical physics at the advanced undergraduate and graduate level.
Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Ilya J. Bakelman
Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Ilya J. Bakelman and published by CRC Press. This book was released on 1993-02-17 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference features papers from the Special Session of the American Mathematical Society Meeting held in 1990 at the University of North Texas, Denton - discussing and developing research on boundary value problems for nonlinear partial differential equations and related problems.;Written by more than 15 authorities in the field, Geometric Analysis and Nonlinear Partial Differential Equations: presents methods and results of the convex bodies and geometric inequalities theory and its applications to differential equations, geometry, and mathematical physics; details recent studies on Monge-Ampere equations, emphasizing geometric inequalities governing a priori estimates of solutions and existence theorems of the Dirichlet problem for convex generalized solutions and showing the proofs of all theorems; examines the generalization of the isoperimetric inequality for two-dimensional general convex surfaces whose integral Gaussian curvature is less than 2 pi; and contains open problems on the theory of surfaces with constant mean curvature.;Geometric Analysis and Nonlinear Partial Differential Equations is for mathematical analysts, geometers, pure and applied mathematicians, physicists, engineers, computer scientists, and upper-level undergraduate and graduate students in these disciplines.
Book Synopsis Stochastic Geometric Analysis With Applications by : Ovidiu Calin
Download or read book Stochastic Geometric Analysis With Applications written by Ovidiu Calin and published by World Scientific. This book was released on 2023-11-21 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive exploration of the interplay between Stochastic Analysis, Geometry, and Partial Differential Equations (PDEs). It aims to investigate the influence of geometry on diffusions induced by underlying structures, such as Riemannian or sub-Riemannian geometries, and examine the implications for solving problems in PDEs, mathematical finance, and related fields. The book aims to unify the relationships between PDEs, nonholonomic geometry, and stochastic processes, focusing on a specific condition shared by these areas known as the bracket-generating condition or Hörmander's condition. The main objectives of the book are:The intended audience for this book includes researchers and practitioners in mathematics, physics, and engineering, who are interested in stochastic techniques applied to geometry and PDEs, as well as their applications in mathematical finance and electrical circuits.
Book Synopsis Hyperbolic Differential Operators And Related Problems by : Vincenzo Ancona
Download or read book Hyperbolic Differential Operators And Related Problems written by Vincenzo Ancona and published by CRC Press. This book was released on 2003-03-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting research from more than 30 international authorities, this reference provides a complete arsenal of tools and theorems to analyze systems of hyperbolic partial differential equations. The authors investigate a wide variety of problems in areas such as thermodynamics, electromagnetics, fluid dynamics, differential geometry, and topology. Renewing thought in the field of mathematical physics, Hyperbolic Differential Operators defines the notion of pseudosymmetry for matrix symbols of order zero as well as the notion of time function. Surpassing previously published material on the topic, this text is key for researchers and mathematicians specializing in hyperbolic, Schrödinger, Einstein, and partial differential equations; complex analysis; and mathematical physics.
Book Synopsis Handbook of Geometric Analysis by : Lizhen Ji
Download or read book Handbook of Geometric Analysis written by Lizhen Ji and published by . This book was released on 2008 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Amperè equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis--the first of the two to be published in the ALM series--presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas."--Back cover.
Book Synopsis Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs by : Alexander Grigor'yan
Download or read book Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs written by Alexander Grigor'yan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Book Synopsis Geometric Analysis of PDE and Several Complex Variables by : Francois Treves
Download or read book Geometric Analysis of PDE and Several Complex Variables written by Francois Treves and published by American Mathematical Soc.. This book was released on 2005 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles generally reflect the interaction of geometry and analysis that is typical of Treves's work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.
Book Synopsis Geometric Analysis by : Joaqun Prez
Download or read book Geometric Analysis written by Joaqun Prez and published by American Mathematical Soc.. This book was released on 2012-07-16 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry.
Book Synopsis Lectures on Nonlinear Hyperbolic Differential Equations by : Lars Hörmander
Download or read book Lectures on Nonlinear Hyperbolic Differential Equations written by Lars Hörmander and published by Springer Science & Business Media. This book was released on 1997-07-17 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this introductory textbook, a revised and extended version of well-known lectures by L. Hörmander from 1986, four chapters are devoted to weak solutions of systems of conservation laws. Apart from that the book only studies classical solutions. Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data. Four chapters are devoted to microanalysis of the singularities of the solutions. This part assumes some familiarity with pseudodifferential operators which are standard in the theory of linear differential operators, but the extension to the more exotic classes of opertors needed in the nonlinear theory is presented in complete detail.
Book Synopsis The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type by : Thomas H. Otway
Download or read book The Dirichlet Problem for Elliptic-Hyperbolic Equations of Keldysh Type written by Thomas H. Otway and published by Springer Science & Business Media. This book was released on 2012-01-07 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems which can be formulated for equations of Keldysh type, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space. Specific applications to plasma physics, optics, and analysis on projective spaces are discussed. (From the preface)
Book Synopsis Hyperbolic Problems and Regularity Questions by : Mariarosaria Padula
Download or read book Hyperbolic Problems and Regularity Questions written by Mariarosaria Padula and published by Birkhäuser. This book was released on 2009-09-03 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics. The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
