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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 Partial Differential Equations by : Andreas Meister
Download or read book Hyperbolic Partial Differential Equations written by Andreas Meister and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives an introduction to the fundamental properties of hyperbolic partial differential equations und their appearance in the mathematical modelling of various problems from practice. It shows in an unique manner concepts for the numerical treatment of such equations starting from basic algorithms up actual research topics in this area. The numerical methods discussed are central and upwind schemes for structured and unstructured grids based on ENO and WENO reconstructions, pressure correction schemes like SIMPLE and PISO as well as asymptotic-induced algorithms for low-Mach number flows.
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 . This book was released on 2015 with total page 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 Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy by :
Download or read book Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM by : John A. Trangenstein
Download or read book Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM written by John A. Trangenstein and published by Cambridge University Press. This book was released on 2013-04-18 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).
Book Synopsis Some Classes of Partial Differential Equations by : Andreĭ Vasilʹevich Bit︠s︡adze
Download or read book Some Classes of Partial Differential Equations written by Andreĭ Vasilʹevich Bit︠s︡adze and published by CRC Press. This book was released on 1988 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic examination of classical and non-classical problems for linear partial differential equations and systems of elliptic, hyperbolic and mixed types. Among a number of difficult problems addressed are the Dirichlet and oblique derivative problems for non- uniformly elliptic equations and non-strongly elliptic systems and the Cauchy and Darloux problems for non-strongly hyperbolic systems and hyperbolic equations with parabolic degeneracy on the boundary. Written at a level suitable for undergraduate and graduate students and researchers. Individual price, $89. Annotation copyrighted by Book News, Inc., Portland, OR
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 Elliptic Partial Differential Equations by : Qing Han
Download or read book Elliptic Partial Differential Equations written by Qing Han and published by American Mathematical Soc.. This book was released on 2011 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Book Synopsis Partial Differential Equations by : Jürgen Jost
Download or read book Partial Differential Equations written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2012-11-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.
Book Synopsis Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy by : Guo Chun Wen
Download or read book Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy written by Guo Chun Wen and published by World Scientific. This book was released on 2008 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the fishing community of Fjallbacka, life is remote, peaceful, and for some, tragically short. Foul play was always suspected in the disappearance twenty years ago of two young campers, but their bodies were never found. But now, a young boy out playing has confirmed the grim truth. Their remains are discovered alongside those of a fresh victim, sending the tiny town into shock. Local detective Patrik Hedstrom, expecting a baby with his girlfriend Erica, can only imagine what it is like to lose a child. When a second young girl goes missing, Hedstrom's attention focuses on the Hults, a feuding clan of misfits, religious fanatics and criminals. The suspect list is long but time is short which of this family's dark secrets will provide the vital clue? Praise for The Ice Princess : The hottest crime genre of the moment is Nordic noir and Swedish writer Camilla Luckberg (who shares Stieg Larsson's translator) is one of the reasons. As with all Scandinavian murder mysteries, it's darker, bleaker, and the plot far more sinister than similar American fare. Larsson fans who give Luckberg's novel a chance to seduce them will be rewarded. USA Today At the start of Luckberg's haunting U.S. debut, biographer Erica Falck feels compelled to write a novel about why her beautiful friend Alex would kill herself. Luckberg skillfully details how horrific secrets are never completely buried and how silence can kill the soul." Publishers Weekly , starred review Camilla Luckberg has written seven blockbuster novels in her native Swedish but, until now, no one has published any of them in the United States. Now Pegasus Books has stepped forward.â¿ â¿¿ The New York Times Heart-stopping a masterclass in Scandinavian crime fiction." Val McDermid
Book Synopsis Hyperbolic Partial Differential Equations by : Peter D. Lax
Download or read book Hyperbolic Partial Differential Equations written by Peter D. Lax and published by American Mathematical Soc.. This book was released on 2006 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
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.
Author :Sylvie Benzoni-Gavage Publisher :Oxford University Press on Demand ISBN 13 :019921123X Total Pages :535 pages Book Rating :4.1/5 (992 download)
Book Synopsis Multi-dimensional Hyperbolic Partial Differential Equations by : Sylvie Benzoni-Gavage
Download or read book Multi-dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and published by Oxford University Press on Demand. This book was released on 2007 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Book Synopsis Partial Differential Equations with Numerical Methods by : Stig Larsson
Download or read book Partial Differential Equations with Numerical Methods written by Stig Larsson and published by Springer Science & Business Media. This book was released on 2008-12-05 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.
Book Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
Download or read book Numerical Methods for Elliptic and Parabolic Partial Differential Equations written by Peter Knabner and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Book Synopsis On Difference Methods for the Solution of a Partial Differential Equation of Mixed Type by : Hajimu Ogawa
Download or read book On Difference Methods for the Solution of a Partial Differential Equation of Mixed Type written by Hajimu Ogawa and published by . This book was released on 1959 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Partial Differential Equations: Finite Difference Methods by : J.W. Thomas
Download or read book Numerical Partial Differential Equations: Finite Difference Methods written by J.W. Thomas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.
