Stability, Instability, and Direct Integrals (Chapman & Hall/CRC Research Notes in Mathematics, #402)
by Bruno Scarpellini
In this masterful study, the author sets forth a unique treatment of the stability and instability of the periodic equilibria of partial differential equations as they relate to the notion of direct integrals. His results, and to a large extent his methods are new. Although he aims this work at theory rather than applications, once the theoretical framework is built, applications emerge with ease.Readers with some basis in functional analysis-notably semigroups-and measure theory can strengthen...
Chemotaxis, Reaction, Network: Mathematics For Self-organization
by Takashi Suzuki
This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:
Half-Linear Differential Equations (North-Holland Mathematics Studies, #202)
by Ondrej Doly and Ondrej Dosly
The book presents a systematic and compact treatment of the qualitative theory of half-linear differential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contain...
Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics
Differential Equations on Singular Manifolds (Mathematical Topics S.)
by Bert-Wolfgang Schulze and etc.
In the book, new methods in the theory of differential equations on manifolds with singularities are presented. The semiclassical theory in quantum mechanics is employed, adapted to operators that are degenerate in a typical way. The degeneracies may be induced by singular geometries, e.g., conical or cuspidal ones. A large variety of non-standard degenerate operators are also discussed. The semiclassical approach yields new results and unexpected effects, also in classical situations. For inst...
Function Theoretic Methods for Partial Differential Equations (Lecture Notes in Mathematics, #561)
Applications Of Nonstandard Finite Difference Schemes
The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations that arise in groundwater poll...
Elements of Partial Differential Equations (Dover Books on Mathematics) (International Series in Pure & Applied Mathematics)
by Ian Naismith Sneddon
Basic Theory of Fractional Differential Equations (Second Edition)
by Yong Zhou and Jinrong Wang Zhang
Inequalities, Entropy and Partial Differential Equations (Pitman Research Notes in Mathematics, No 295)
by W A Day
Non-Standard and Improperly Posed Problems (Mathematics in Science and Engineering)
by Karen A Ames, Brian Straughan, and William F. Ames
Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and...
Stochastic Partial Differential Equations for Computer Vision with Uncertain Data (Synthesis Lectures on Visual Computing)
by Tobias Preusser, Robert M. Kirby, and Torben Patz
In image processing and computer vision applications such as medical or scientific image data analysis, as well as in industrial scenarios, images are used as input measurement data. It is good scientific practice that proper measurements must be equipped with error and uncertainty estimates. For many applications, not only the measured values but also their errors and uncertainties, should be-and more and more frequently are-taken into account for further processing. This error and uncertainty...
Fractional Differential Equations (Mathematics in Science and Engineering)
by Igor Podlubny
This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adeq...
This work is designed as an introduction to the concepts of modern differential analysis applied to partial differential equations. It contains numerous practical problems/solutions. This third edition incorporates new material on boundary elements, spectral methods, the methods of lines and invariant methods. At the same time, the material on finite elements and finite differences have been merged and given equal weight. The text is suitable for PDE courses.
Introduction to Partial Differentia
by Donald Greenspan and Mathematics
Wavefronts And Rays As Characteristics And Asymptotics (Third Edition)
by Andrej Bona and Michael A Slawinski
Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limita...
Harmonic Analysis And Wave Equations (Series in Contemporary Applied Mathematics, #23)
This book is a collection of lecture notes for the LIASFMA School and Workshop on 'Harmonic Analysis and Wave Equations' which was held on May 8-18, 2017 at Fudan University, in Shanghai, China. The aim of the LIASFMA School and Workshop is to bring together Chinese and French experts to discuss and dissect recent progress in these related fields; and to disseminate state of art, new knowledge and new concepts, to graduate students and junior researchers.The book provides the readers with a uniq...
This volume consists of the proceedings of the conference on Physical Mathematics and Nonlinear Partial Differential Equations held at West Virginia University in Morgantown. It describes some work dealing with weak limits of solutions to nonlinear systems of partial differential equations.
Partial Differential Equations
by Walter A Strauss, Julie L. Levandosky, and Steven P. Levandosky
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 impor...
The Solution of Partial Differential Equations by Finite Difference Approximations
by Lewis Hall Msc