Partial Differential Equations in Mechanics 1

Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation


Author: A.P.S. Selvadurai

Publisher: Springer Science & Business Media

ISBN: 9783540672838

Category: Mathematics

Page: 595

View: 828

"Por he who knows not mathematics cannot know any other sciences; what is more, he cannot discover his own ignorance or find its proper remedies. " [Opus Majus] Roger Bacon (1214-1294) The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations. The impetus for writing these volumes was the opportunity to teach the subject matter to both undergraduate and graduate students in engineering at several universi ties. The approach is distinctly different to that wh ich would adopted should such a course be given to students in pure mathematics; in this sense, the teaching of partial differential equations within an engineering curriculum should be viewed in the broader perspective of "The Modelling 0/ Problems in Engineering" . An engineering student should be given the opportunity to appreciate how the various combination of balance laws, conservation equations, kinematic constraints, constitutive responses, thermodynamic re strictions, etc. , culminates in the development of a partial differential equa tion, or sets of partial differential equations, with potential for applications to engineering problems. This ability to distill all the diverse information about a physical or mechanical process into partial differential equations is a particular attraction of the subject area.

Partial Differential Equations in Mechanics 2

The Biharmonic Equation, Poisson’s Equation


Author: A.P.S. Selvadurai

Publisher: Springer Science & Business Media

ISBN: 3662092050

Category: Technology & Engineering

Page: 698

View: 2596

This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Computational Methods for PDE in Mechanics


Author: Berardino D'Acunto

Publisher: World Scientific

ISBN: 9789812560377

Category: Science

Page: 278

View: 9734

- An application-oriented introduction to computational numerical methods for PDE - Complete with numerous exercise sets and solutions - Includes Windows programs in C++ language

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics


Author: Victor A. Galaktionov,Sergey R. Svirshchevskii

Publisher: CRC Press

ISBN: 9781584886631

Category: Mathematics

Page: 528

View: 4046

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.

Advances in Applied Mechanics

Author and Subject Cumulative Index Including, Tables of Content


Author: N.A

Publisher: Academic Press

ISBN: 9780080564135

Category: Science

Page: 332

View: 9644

This highly acclaimed series provides survey articles on the present state and future direction of research in important branches of applied mechanics.

Higher Order Partial Differential Equations in Clifford Analysis

Effective Solutions to Problems


Author: Elena Irodionovna Obolashvili

Publisher: Springer Science & Business Media

ISBN: 9780817642860

Category: Mathematics

Page: 178

View: 833

This monograph is devoted to new types of higher order PDEs in the framework of Clifford analysis. While elliptic and hyperbolic equations have been studied in the Clifford analysis setting in book and journal literature, parabolic equations have been ignored and are the primary focus of this work. These new equations have remarkable applications to mathematical physics---mechanics of deformable bodies, electromagnetic fields, quantum mechanics. Book will appeal to mathematicians and physicists in PDEs, and it may also be used as a supplementary text by graduate students.

Spectral and High Order Methods for Partial Differential Equations

Selected papers from the ICOSAHOM '09 conference, June 22-26, Trondheim, Norway


Author: Jan S. Hesthaven,Einar M. Rønquist

Publisher: Springer Science & Business Media

ISBN: 9783642153372

Category: Mathematics

Page: 510

View: 3487

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2009), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.

Partial Differential Equations and Fluid Mechanics


Author: James C. Robinson

Publisher: Cambridge University Press

ISBN: 052112512X

Category: Mathematics

Page: 257

View: 5741

Recent years have seen considerable research activity at the interface of mathematics and fluid mechanics, particularly partial differential equations. The 2007 workshop at the University of Warwick was organised to consolidate, survey and further advance the subject. This volume is an outgrowth of that workshop. It consists of a number of reviews and a selection of more traditional research articles. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves as both a helpful overview for graduate students new to the area and a useful resource for more established researchers.