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Author : Pierre Grisvard
Release : 1992
Genre : Boundary value problems
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Singularities in Boundary Value Problems by : Pierre Grisvard
Download or read book Singularities in Boundary Value Problems written by Pierre Grisvard. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt:
Author : H.G. Garnir
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 340/5 ( reviews)
Book Synopsis Singularities in Boundary Value Problems by : H.G. Garnir
Download or read book Singularities in Boundary Value Problems written by H.G. Garnir. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The 1980 Maratea NATO Advanced Study Institute (= ASI) followed the lines of the 1976 Liege NATO ASI. Indeed, the interest of boundary problems for linear evolution partial differential equations and systems is more and more acute because of the outstanding position of those problems in the mathematical description of the physical world, namely through sciences such as fluid dynamics, elastodynamics, electro dynamics, electromagnetism, plasma physics and so on. In those problems the question of the propagation of singularities of the solution has boomed these last years. Placed in its definitive mathematical frame in 1970 by L. Hormander, this branch -of the theory recorded a tremendous impetus in the last decade and is now eagerly studied by the most prominent research workers in the field of partial differential equations. It describes the wave phenomena connected with the solution of boundary problems with very general boundaries, by replacing the (generailly impossible) computation of a precise solution by a convenient asymptotic approximation. For instance, it allows the description of progressive waves in a medium with obstacles of various shapes, meeting classical phenomena as reflexion, refraction, transmission, and even more complicated ones, called supersonic waves, head waves, creeping waves, •••••• The !'tudy of singularities uses involved new mathematical concepts (such as distributions, wave front sets, asymptotic developments, pseudo-differential operators, Fourier integral operators, microfunctions, ••• ) but emerges as the most sensible application to physical problems. A complete exposition of the present state of this theory seemed to be still lacking.
Author : Vladimir Kozlov
Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : 544/5 ( reviews)
Book Synopsis Elliptic Boundary Value Problems in Domains with Point Singularities by : Vladimir Kozlov
Download or read book Elliptic Boundary Value Problems in Domains with Point Singularities written by Vladimir Kozlov. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: For graduate students and research mathematicians interested in partial differential equations and who have a basic knowledge of functional analysis. Restricted to boundary value problems formed by differential operators, avoiding the use of pseudo- differential operators. Concentrates on fundamental results such as estimates for solutions in different function spaces, the Fredholm property of the problem's operator, regularity assertions, and asymptotic formulas for the solutions of near singular points. Considers the solutions in Sobolev spaces of both positive and negative orders. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Zohar Yosibash
Release : 2011-12-02
Genre : Mathematics
Kind : eBook
Book Rating : 08X/5 ( reviews)
Book Synopsis Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation by : Zohar Yosibash
Download or read book Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation written by Zohar Yosibash. This book was released on 2011-12-02. Available in PDF, EPUB and Kindle. Book excerpt: This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.
Author : Donal O'regan
Release : 1994-04-29
Genre : Mathematics
Kind : eBook
Book Rating : 006/5 ( reviews)
Book Synopsis Theory Of Singular Boundary Value Problems by : Donal O'regan
Download or read book Theory Of Singular Boundary Value Problems written by Donal O'regan. This book was released on 1994-04-29. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys some topics in the rapidly developing areas of regular and singular boundary value problems. It also provides a detailed account of the current state of the literature on existence theory for ordinary differential equations. Results are presented for finite and semi-infinite intervals. Singularities in both independent and dependent variables are discussed.
