Nonlinear Parabolic Equations and Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Parabolic Equations and Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76 write by Songmu Zheng. This book was released on 1995-04-01. Nonlinear Parabolic Equations and Hyperbolic Parab Olic Coupled Systems Pitman Monographs 76 available in PDF, EPUB and Kindle.
Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems
Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems write by Songmu Zheng. This book was released on 2019-12-02. Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems available in PDF, EPUB and Kindle. 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.
Functional Inequalities: New Perspectives and New Applications
Functional Inequalities: New Perspectives and New Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Functional Inequalities: New Perspectives and New Applications write by Nassif Ghoussoub. This book was released on 2013-04-09. Functional Inequalities: New Perspectives and New Applications available in PDF, EPUB and Kindle. "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
Clifford Algebras and Their Applications in Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebras and Their Applications in Mathematical Physics write by J.S.R. Chisholm. This book was released on 2012-12-06. Clifford Algebras and Their Applications in Mathematical Physics available in PDF, EPUB and Kindle. 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
Probabilistic Properties of Deterministic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probabilistic Properties of Deterministic Systems write by Andrzej Lasota. This book was released on 2008-11-27. Probabilistic Properties of Deterministic Systems available in PDF, EPUB and Kindle. 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.
