Partial Differential Equations With Minimal Smoothness And Applications

Author : B Dahlberg,Eugene Fabes,R Fefferman
Publisher : Unknown
Page : 240 pages
File Size : 48,6 Mb
Release : 1992-03-12
Category : Electronic
ISBN : 1461228999

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Partial Differential Equations with Minimal Smoothness and Applications by B Dahlberg,Eugene Fabes,R Fefferman Pdf

In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.

Author : B. Dahlberg,Eugene Fabes,R. Fefferman,David Jerison,Carlos Kenig,J. Pipher
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461228981

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Partial Differential Equations with Minimal Smoothness and Applications by B. Dahlberg,Eugene Fabes,R. Fefferman,David Jerison,Carlos Kenig,J. Pipher Pdf

In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.

Author : Michael Shearer,Rachel Levy
Publisher : Princeton University Press
Page : 286 pages
File Size : 44,6 Mb
Release : 2015-03-01
Category : Mathematics
ISBN : 9780691161297

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Partial Differential Equations by Michael Shearer,Rachel Levy Pdf

An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 55,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821868898

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Partial Differential Equations and Boundary-Value Problems with Applications by Mark A. Pinsky Pdf

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.

Author : Boško S. Jovanović,Endre Süli
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 45,9 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781447154600

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Analysis of Finite Difference Schemes by Boško S. Jovanović,Endre Süli Pdf

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Author : Piero Bassanini,Alan R. Elcrat
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 51,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489918758

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Theory and Applications of Partial Differential Equations by Piero Bassanini,Alan R. Elcrat Pdf

This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.

Author : Peter Charles Greiner,Canadian Mathematical Society. Seminar
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 44,6 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0821870149

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Partial Differential Equations and Their Applications by Peter Charles Greiner,Canadian Mathematical Society. Seminar Pdf

Just list for purposes of NBB.

Author : Robert C. McOwen
Publisher : 清华大学出版社有限公司
Page : 446 pages
File Size : 42,7 Mb
Release : 2004
Category : Differential equations, Partial
ISBN : 7302099804

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Partial Differential Equations by Robert C. McOwen Pdf

Author : Louis Dupaigne
Publisher : CRC Press
Page : 337 pages
File Size : 45,7 Mb
Release : 2011-03-15
Category : Mathematics
ISBN : 9781420066548

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Stable Solutions of Elliptic Partial Differential Equations by Louis Dupaigne Pdf

Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics (combustion, phase transition theory) and geometry (minimal surfaces). Stable Solutions of Elliptic Partial Differential Equations offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The central questions of regularity and classification of stable solutions are treated at length. Specialists will find a summary of the most recent developments of the theory, such as nonlocal and higher-order equations. For beginners, the book walks you through the fine versions of the maximum principle, the standard regularity theory for linear elliptic equations, and the fundamental functional inequalities commonly used in this field. The text also includes two additional topics: the inverse-square potential and some background material on submanifolds of Euclidean space.

Author : Dorina Mitrea,Marius Mitrea
Publisher : American Mathematical Soc.
Page : 446 pages
File Size : 44,9 Mb
Release : 2008
Category : Differential equations, Partial
ISBN : 9780821844243

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Perspectives in Partial Differential Equations, Harmonic Analysis and Applications by Dorina Mitrea,Marius Mitrea Pdf

This volume contains a collection of papers contributed on the occasion of Mazya's 70th birthday by a distinguished group of experts of international stature in the fields of harmonic analysis, partial differential equations, function theory, and spectral analysis, reflecting the state of the art in these areas.

Author : Mark A. Pinsky
Publisher : McGraw-Hill Companies
Page : 344 pages
File Size : 46,5 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015018344997

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Introduction to Partial Differential Equations with Applications by Mark A. Pinsky Pdf

Author : A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso
Publisher : CRC Press
Page : 236 pages
File Size : 51,6 Mb
Release : 1996-05-15
Category : Mathematics
ISBN : 0582259703

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Progress in Elliptic and Parabolic Partial Differential Equations by A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso Pdf

This Research Note collects reports of the invited plenary addresses given during the conference Elliptic and Parabolic Partial Differential Equations and Applications held in Capri, Italy, 19-23 September 1994. The conference was devoted to new developments in partial differential equations of elliptic and parabolic type and to their applications in various fields.

Author : Nikos Katzourakis
Publisher : Springer
Page : 123 pages
File Size : 48,8 Mb
Release : 2014-11-26
Category : Mathematics
ISBN : 9783319128290

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An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞ by Nikos Katzourakis Pdf

The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.

Author : J. Necas
Publisher : Routledge
Page : 188 pages
File Size : 42,6 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351425865

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Partial Differential Equations by J. Necas Pdf

As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in numerical methods in their fields. Conference organizers chose the contributors to bring together the scientists best able to present a complex view of problems, starting from the modeling, passing through the mathematical treatment, and ending with numerical realization. The applications discussed include fluid dynamics, semiconductor technology, image analysis, motion analysis, and optimal control. The importance and quantity of research carried out around the world in this field makes it imperative for researchers, applied mathematicians, physicists and engineers to keep up with the latest developments. With its panel of international contributors and survey of the recent ramifications of theory, applications, and numerical methods, Partial Differential Equations: Theory and Numerical Solution provides a convenient means to that end.

Author : Boling Guo,Dadi Yang
Publisher : World Scientific
Page : 268 pages
File Size : 53,6 Mb
Release : 1998-10-30
Category : Electronic
ISBN : 9789814544269

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Nonlinear Partial Differential Equations and Applications by Boling Guo,Dadi Yang Pdf

Contents: Direct and Inverse Diffraction by Periodic Structures (G Bao)Weak Flow of H-Systems (Y-M Chen)Strongly Compact Attractor for Dissipative Zakharov Equations (B-L Guo et al.)C∞-Solutions of Generalized Porous Medium Equations (M Ôtani & Y Sugiyama)Cauchy Problem for Generalized IMBq Equation (G-W Chen & S-B Wang)Inertial Manifolds for a Nonlocal Kuramoto–Sivashinsky Equation (J-Q Duan et al.)Weak Solutions of the Generalized Magnetic Flow Equations (S-H He & Z-D Dai)The Solution of Hammerstein Integral Equation Without Coercive Conditions (Y-L Shu)Global Behaviour of the Solution of Nonlinear Forest Evolution Equation (D-J Wang)Uniqueness of Generalized Solutions for Semiconductor Equations (J-S Xing & Y Hu)On the Vectorial Hamilton–Jacobi System (B-S Yan)An Integrable Hamiltonian System Associated with cKdV Hierarchy (J-S Zhang et al.)and other papers Readership: Mathematicians. Keywords:Diffraction;Weak Flow;Zakharov Equations;Porous Medium Equations;Cauchy Problem;IMBq Equation;Kuramoto-Sivashinsky Equation;Magnetic Flow Equations;Hammerstein Integral Equation;Nonlinear Forest Evolution Equation;Uniqueness;Generalized Solutions;Semiconductor Equations;Hamilton–Jacobi System;Hamiltonian System;cKdV Hierarchy