Analytic Inequalities and Their Applications in PDEs
Analytic Inequalities and Their Applications in PDEs

Author: Yuming Qin

Publisher: Birkhäuser

Published: 2017-02-13

Total Pages: 570

ISBN-13: 3319008315

DOWNLOAD EBOOK

This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.

Approximation Theory and Analytic Inequalities
Approximation Theory and Analytic Inequalities

Author: Themistocles M. Rassias

Publisher: Springer Nature

Published: 2021-07-21

Total Pages: 546

ISBN-13: 3030606228

DOWNLOAD EBOOK

This contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.

Nonlinear Partial Differential Equations with Applications
Nonlinear Partial Differential Equations with Applications

Author: Tomás Roubicek

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 415

ISBN-13: 3764373970

DOWNLOAD EBOOK

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

Harnack Inequalities for Stochastic Partial Differential Equations
Harnack Inequalities for Stochastic Partial Differential Equations

Author: Feng-Yu Wang

Publisher: Springer Science & Business Media

Published: 2013-08-13

Total Pages: 135

ISBN-13: 1461479347

DOWNLOAD EBOOK

​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Evolution Equations, Feshbach Resonances, Singular Hodge Theory
Evolution Equations, Feshbach Resonances, Singular Hodge Theory

Author: Michael Demuth

Publisher: Wiley-VCH

Published: 1999-04-22

Total Pages: 436

ISBN-13:

DOWNLOAD EBOOK

Evolution equations describe many processes in science and engineering, and they form a central topic in mathematics. The first three contributions to this volume address parabolic evolutionary problems: The opening paper treats asymptotic solutions to singular parabolic problems with distribution and hyperfunction data. The theory of the asymptotic Laplace transform is developed in the second paper and is applied to semigroups generated by operators with large growth of the resolvent. An article follows on solutions by local operator methods of time-dependent singular problems in non-cylindrical domains. The next contribution addresses spectral properties of systems of pseudodifferential operators when the characteristic variety has a conical intersection. Bohr-Sommerfeld quantization rules and first order exponential asymptotics of the resonance widths are established under various semiclassical regimes. In the following article, the limiting absorption principle is proven for certain self-adjoint operators. Applications include Hamiltonians with magnetic fields, Dirac Hamiltonians, and the propagation of waves in inhomogeneous media. The final topic develops Hodge theory on manifolds with edges; its authors introduce a concept of elliptic complexes, prove a Hodge decomposition theorem, and study the asymptotics of harmonic forms.

Inequalities and Applications
Inequalities and Applications

Author: Catherine Bandle

Publisher: Springer Science & Business Media

Published: 2008-12-17

Total Pages: 330

ISBN-13: 3764387734

DOWNLOAD EBOOK

Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and Pólya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics. This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.

Functional Analysis, Sobolev Spaces and Partial Differential Equations
Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author: Haim Brezis

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 600

ISBN-13: 0387709142

DOWNLOAD EBOOK

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Partial Differential Equations
Partial Differential Equations

Author: Walter A. Strauss

Publisher: John Wiley & Sons

Published: 2007-12-21

Total Pages: 467

ISBN-13: 0470054565

DOWNLOAD EBOOK

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Numerical Analysis of Partial Differential Equations
Numerical Analysis of Partial Differential Equations

Author: S. H, Lui

Publisher: John Wiley & Sons

Published: 2012-01-10

Total Pages: 506

ISBN-13: 1118111117

DOWNLOAD EBOOK

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.