On Dirichlet's Boundary Value Problem
Author: Christian G. Simader
Publisher: Springer
Published: 2006-11-15
Total Pages: 243
ISBN-13: 3540375899
DOWNLOAD EBOOKPosts
A Unified Approach to Boundary Value Problems
Author: Athanassios S. Fokas
Publisher: SIAM
Published: 2008-01-01
Total Pages: 328
ISBN-13: 089871706X
DOWNLOAD EBOOKThis 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
Published: 2020-01-03
Total Pages: 775
ISBN-13: 3030367142
DOWNLOAD EBOOKThis 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.
Perturbation of the Boundary in Boundary-Value Problems of Partial Differential Equations
Author: Dan Henry
Publisher: Cambridge University Press
Published: 2005-05-26
Total Pages: 220
ISBN-13: 9781139441179
DOWNLOAD EBOOKPerturbation 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.
Polyharmonic Boundary Value Problems
Author: Filippo Gazzola
Publisher: Springer
Published: 2010-05-26
Total Pages: 444
ISBN-13: 3642122450
DOWNLOAD EBOOKThis 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.
Hodge Decomposition - A Method for Solving Boundary Value Problems
Author: Günter Schwarz
Publisher: Springer
Published: 2006-11-14
Total Pages: 161
ISBN-13: 3540494030
DOWNLOAD EBOOKHodge 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
Published: 2018-03-31
Total Pages: 669
ISBN-13: 3319743074
DOWNLOAD EBOOKThis 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.
Elliptic Differential Equations
Author: W. Hackbusch
Publisher: Springer Science & Business Media
Published: 1992
Total Pages: 334
ISBN-13: 9783540548225
DOWNLOAD EBOOKDerived from a lecture series for college mathematics students, introduces the methods of dealing with elliptical boundary-value problems--both the theory and the numerical analysis. Includes exercises. Translated and somewhat expanded from the 1987 German version. Annotation copyright by Book News, Inc., Portland, OR
Initial-boundary Value Problems and the Navier-Stokes Equations
Author: Heinz-Otto Kreiss
Publisher: SIAM
Published: 1989-01-01
Total Pages: 408
ISBN-13: 0898719135
DOWNLOAD EBOOKAnnotation 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.
Lectures on Partial Differential Equations
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 168
ISBN-13: 3662054418
DOWNLOAD EBOOKChoice 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.
