On Dirichlet's Boundary Value Problem
Author : Christian G. Simader
Publisher : Springer
Page : 243 pages
File Size : 43,90 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540375899
A Unified Approach to Boundary Value Problems
Author : Athanassios S. Fokas
Publisher : SIAM
Page : 328 pages
File Size : 32,85 MB
Release : 2008-01-01
Category : Mathematics
ISBN : 089871706X
Book Description
This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Boundary Value Problems, Weyl Functions, and Differential Operators
Author : Jussi Behrndt
Publisher : Springer Nature
Page : 775 pages
File Size : 14,6 MB
Release : 2020-01-03
Category : Mathematics
ISBN : 3030367142
Book Description
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Initial-boundary Value Problems and the Navier-Stokes Equations
Author : Heinz-Otto Kreiss
Publisher : SIAM
Page : 408 pages
File Size : 37,13 MB
Release : 1989-01-01
Category : Science
ISBN : 0898719135
Book Description
Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
Hodge Decomposition - A Method for Solving Boundary Value Problems
Author : Günter Schwarz
Publisher : Springer
Page : 161 pages
File Size : 23,94 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540494030
Book Description
Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.
The Laplace Equation
Author : Dagmar Medková
Publisher : Springer
Page : 669 pages
File Size : 19,92 MB
Release : 2018-03-31
Category : Mathematics
ISBN : 3319743074
Book Description
This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics. This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.
Polyharmonic Boundary Value Problems
Author : Filippo Gazzola
Publisher : Springer
Page : 444 pages
File Size : 46,65 MB
Release : 2010-05-26
Category : Mathematics
ISBN : 3642122450
Book Description
This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations
Author : Dan Henry
Publisher : Cambridge University Press
Page : 220 pages
File Size : 20,21 MB
Release : 2005-05-26
Category : Mathematics
ISBN : 9781139441179
Book Description
Perturbation of the boundary is a rather neglected topic in the study of partial differential equations, in part because it often entails long and difficult caluclations. In this book, first published in 2005, the author carefully discusses a calculus that overcomes the computational morass, and he goes on to develop more general forms of standard theorems, helping to answer a problems involving boundary perturbations.
Lectures on Partial Differential Equations
Author : Vladimir I. Arnold
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 21,3 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662054418
Book Description
Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.
Partial Differential Equations and Boundary-Value Problems with Applications
Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 32,39 MB
Release : 2011
Category : Mathematics
ISBN : 0821868896
Book Description
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
