Spherical Means for PDEs PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Spherical Means for PDEs PDF full book. Access full book title Spherical Means for PDEs by Karl K. Sabelfeld. Download full books in PDF and EPUB format.
Author: Karl K. Sabelfeld
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926024
Category : Mathematics
Languages : en
Pages : 196
Get Book Here
Book Description
This monographs presents new spherical mean value relations for classical boundary value problems of mathematical physics. The derived spherical mean value relations provide equivalent integral formulations of original boundary value problems. Direct and converse mean value theorems are proved for scalar elliptic equations (the Laplace, Helmholtz and diffusion equations), parabolic equations, high-order elliptic equations (biharmonic and metaharmonic equations), and systems of elliptic equations (the Lami equation, systems of diffusion and elasticity equations). In addition, applications to the random walk on spheres method are given.
Author: Karl K. Sabelfeld
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926024
Category : Mathematics
Languages : en
Pages : 196
Get Book Here
Book Description
This monographs presents new spherical mean value relations for classical boundary value problems of mathematical physics. The derived spherical mean value relations provide equivalent integral formulations of original boundary value problems. Direct and converse mean value theorems are proved for scalar elliptic equations (the Laplace, Helmholtz and diffusion equations), parabolic equations, high-order elliptic equations (biharmonic and metaharmonic equations), and systems of elliptic equations (the Lami equation, systems of diffusion and elasticity equations). In addition, applications to the random walk on spheres method are given.
Author: F. John
Publisher: Springer Science & Business Media
ISBN: 1461394538
Category : Mathematics
Languages : en
Pages : 174
Get Book Here
Book Description
The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form. New Rochelle FRITZ JOHN September, 1955 [v] CONTENTS Introduction. . . . . . . 1 CHAPTER I Decomposition of an Arbitrary Function into Plane Waves Explanation of notation . . . . . . . . . . . . . . . 7 The spherical mean of a function of a single coordinate. 7 9 Representation of a function by its plane integrals . CHAPTER II Tbe Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients Hyperbolic equations. . . . . . . . . . . . . . . . . . . . . . 15 Geometry of the normal surface for a strictly hyperbolic equation. 16 Solution of the Cauchy problem for a strictly hyperbolic equation . 20 Expression of the kernel by an integral over the normal surface. 23 The domain of dependence . . . . . . . . . . . . . . . . . . . 29 The wave equation . . . . . . . . . . . . . . . . . . . . . . 32 The initial value problem for hyperbolic equations with a normal surface having multiple points . . . . . . . . . . . . . . . . . . . . 36 CHAPTER III The Fundamental Solution of a Linear Elliptic Differential Equation witL Analytic Coefficients Definition of a fundamental solution . . . . . . . . . . . . . . 43 The Cauchy problem . . . . . . . . . . . . . . . . . . . . . 45 Solution of the inhomogeneous equation with a plane wave function as right hand side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 The fundamental solution. . . . . . . . . . . . . . . . . . . . . .
Author: Fritz John
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 188
Get Book Here
Book Description
Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
Get Book Here
Book Description
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.
Author: Karl K. Sabel'fel'd
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
Get Book Here
Book Description
Author: Karl K. Sabelfeld
Publisher: Walter de Gruyter
ISBN: 3110315335
Category : Mathematics
Languages : en
Pages : 338
Get Book Here
Book Description
The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.
Author: M. A. Shubin
Publisher: Springer Verlag
ISBN: 9783540520030
Category : Mathematics
Languages : en
Pages : 216
Get Book Here
Book Description
Two general questions regarding partial differential equations are explored in detail in this volume of the Encyclopaedia. The first is the Cauchy problem, and its attendant question of well-posedness (or correctness). The authors address this question in the context of PDEs with constant coefficients and more general convolution equations in the first two chapters. The third chapter extends a number of these results to equations with variable coefficients. The second topic is the qualitative theory of second order linear PDEs, in particular, elliptic and parabolic equations. Thus, the second part of the book is primarily a look at the behavior of solutions of these equations. There are versions of the maximum principle, the Phragmen-Lindel]f theorem and Harnack's inequality discussed for both elliptic and parabolic equations. The book is intended for readers who are already familiar with the basic material in the theory of partial differential equations.
Author: Emmanuele DiBenedetto
Publisher: Springer Science & Business Media
ISBN: 1489928405
Category : Mathematics
Languages : en
Pages : 430
Get Book Here
Book Description
This text is meant to be a self-contained, elementary introduction to Partial Differential Equations, assuming only advanced differential calculus and some basic LP theory. Although the basic equations treated in this book, given its scope, are linear, we have made an attempt to approach them from a nonlinear perspective. Chapter I is focused on the Cauchy-Kowaleski theorem. We discuss the notion of characteristic surfaces and use it to classify partial differential equations. The discussion grows out of equations of second order in two variables to equations of second order in N variables to p.d.e.'s of any order in N variables. In Chapters II and III we study the Laplace equation and connected elliptic theory. The existence of solutions for the Dirichlet problem is proven by the Perron method. This method clarifies the structure ofthe sub(super)harmonic functions and is closely related to the modern notion of viscosity solution. The elliptic theory is complemented by the Harnack and Liouville theorems, the simplest version of Schauder's estimates and basic LP -potential estimates. Then, in Chapter III, the Dirichlet and Neumann problems, as well as eigenvalue problems for the Laplacian, are cast in terms of integral equations. This requires some basic facts concerning double layer potentials and the notion of compact subsets of LP, which we present.
Author: Rustum Choksi
Publisher: American Mathematical Society
ISBN: 1470464918
Category : Mathematics
Languages : en
Pages : 647
Get Book Here
Book Description
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment. The book is rich with physical motivations and interpretations, and it takes special care to clearly explain all the technical mathematical arguments, often with pre-motivations and post-reflections. Through these arguments the reader will develop a deeper proficiency and understanding of advanced calculus. While the text is comprehensive, the material is divided into short sections, allowing particular issues/topics to be addressed in a concise fashion. Sections which are more fundamental to the text are highlighted, allowing the instructor several alternative learning paths. The author's unique pedagogical style also makes the text ideal for self-learning.
Author: Fritz John
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 188
Get Book Here
Book Description
