Nonlinear Parabolic Equations And Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76
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Nonlinear Parabolic Equations And Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76
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Author : Songmu Zheng
language : en
Publisher: Longman Sc & Tech
Release Date : 1995-04-01
Nonlinear Parabolic Equations And Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76 written by Songmu Zheng and has been published by Longman Sc & Tech this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-01 with Mathematics categories.
Nonlinear Parabolic Equations And Hyperbolic Parabolic Coupled Systems
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Author : Songmu Zheng
language : en
Publisher: CRC Press
Release Date : 2020-05-05
Nonlinear Parabolic Equations And Hyperbolic Parabolic Coupled Systems written by Songmu Zheng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.
Nonlinear Parabolic Hyperbolic Coupled Systems And Their Attractors
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Author : Yuming Qin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-25
Nonlinear Parabolic Hyperbolic Coupled Systems And Their Attractors written by Yuming Qin 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 2008-11-25 with Mathematics categories.
This book presents recent results concerning the global existence in time, the large-time behavior, decays of solutions and the existence of global attractors for nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations.
Global Well Posedness Of Nonlinear Parabolic Hyperbolic Coupled Systems
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Author : Yuming Qin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-28
Global Well Posedness Of Nonlinear Parabolic Hyperbolic Coupled Systems written by Yuming Qin 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 2012-02-28 with Mathematics categories.
This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science.
Functional Inequalities New Perspectives And New Applications
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Author : Nassif Ghoussoub
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-09
Functional Inequalities New Perspectives And New Applications written by Nassif Ghoussoub 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 2013-04-09 with Mathematics categories.
"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.
Clifford Algebras And Their Applications In Mathematical Physics
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Author : J.S.R. Chisholm
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Clifford Algebras And Their Applications In Mathematical Physics written by J.S.R. Chisholm 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 Mathematics categories.
William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann's algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley's book, 'The Algebraic Theory of Spinors' in 1954, and of Marcel Riesz' Maryland Lectures in 1959. Some of the contributors to this volume, Georges Deschamps, Erik Folke Bolinder, Albert Crumeyrolle and David Hestenes were working in this field around that time, and in their turn have persuaded others of the importance of the subject.
Probabilistic Properties Of Deterministic Systems
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Author : Andrzej Lasota
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
Probabilistic Properties Of Deterministic Systems written by Andrzej Lasota 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 2008-11-27 with Mathematics categories.
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Monotone Dynamical Systems An Introduction To The Theory Of Competitive And Cooperative Systems
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Author : Hal L. Smith
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Monotone Dynamical Systems An Introduction To The Theory Of Competitive And Cooperative Systems written by Hal L. Smith 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 1995 with Mathematics categories.
This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed. Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.
Computer Literature Bibliography
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Author : United States. National Bureau of Standards
language : en
Publisher:
Release Date : 1965
Computer Literature Bibliography written by United States. National Bureau of Standards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Computers categories.
Variational Methods In Optimization
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Author : Donald R. Smith
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01
Variational Methods In Optimization written by Donald R. Smith and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.