Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data - Couverture rigide
Synopsis
In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be- sides being quite spontaneous, allows us to consider a great many inter- esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis- tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub- sequent developments.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Autres éditions populaires du même titre
Résultats de recherche pour Boundary Value Problems of Finite Elasticity: Local...
Image d'archives
Boundary Value Problems of Finite Elasticity/Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data
Vendeur : Basi6 International, Irving, TX, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Etat : Brand New. New. US edition. Expediting shipping for all USA and Europe orders excluding PO Box. Excellent Customer Service. N° de réf. du vendeur ABEOCT25-86404
Acheter neuf
EUR 69,13
Livraison gratuite
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 1 disponible(s)
Image d'archives
Boundary Value Problems of Finite Elasticity/Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data
Vendeur : Romtrade Corp., STERLING HEIGHTS, MI, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Etat : New. This is a Brand-new US Edition. This Item may be shipped from US or any other country as we have multiple locations worldwide. N° de réf. du vendeur ABBB-153801
Acheter neuf
EUR 69,13
Livraison gratuite
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 1 disponible(s)
Image fournie par le vendeur
Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data. (= Springer tracts in natural philosophy, Volume 31).
Edité par
Springer, New York, 1988
ISBN 10 : 0387965505
ISBN 13 : 9780387965505
Ancien ou d'occasion
Couverture rigide
Vendeur : Antiquariat Silvanus - Inhaber Johannes Schaefer, Ahrbrück, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
191 S., 0387965505 Sprache: Englisch Gewicht in Gramm: 450 Groß 8°, Original-Pappband (Hardcover), Bibliotheks-Exemplar (ordungsgemäß entwidmet), Stempel auf Titel, Rücken leicht aufgehellt, insgesamt gutes und innen sauberes Exemplar, N° de réf. du vendeur 60366
Acheter D'occasion
EUR 32,50
Expédition à EUR 45,90
Expédition depuis Allemagne vers Etats-Unis
Expédition depuis Allemagne vers Etats-Unis
Quantité disponible : 1 disponible(s)
Image d'archives
Boundary Value Problems of Finite Elasticity
Edité par
Springer, 1987
ISBN 10 : 0387965505
ISBN 13 : 9780387965505
Ancien ou d'occasion
Couverture rigide
Vendeur : Books Puddle, New York, NY, Etats-Unis
Évaluation du vendeur 4 sur 5 étoiles
Etat : Used. pp. xii + 191. N° de réf. du vendeur 263125878
Acheter D'occasion
EUR 85,13
Expédition à EUR 3,51
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 1 disponible(s)
Image d'archives
Boundary Value Problems of Finite Elasticity
Edité par
Springer, 1987
ISBN 10 : 0387965505
ISBN 13 : 9780387965505
Ancien ou d'occasion
Couverture rigide
Vendeur : Majestic Books, Hounslow, Royaume-Uni
Évaluation du vendeur 4 sur 5 étoiles
Etat : Used. pp. xii + 191. N° de réf. du vendeur 5770665
Acheter D'occasion
EUR 84,81
Expédition à EUR 7,61
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : 1 disponible(s)
Image d'archives
Boundary Value Problems of Finite Elasticity
Edité par
Springer, 1987
ISBN 10 : 0387965505
ISBN 13 : 9780387965505
Ancien ou d'occasion
Couverture rigide
Vendeur : Biblios, Frankfurt am main, HESSE, Allemagne
Évaluation du vendeur 4 sur 5 étoiles
Etat : Used. pp. xii + 191. N° de réf. du vendeur 183125884
Acheter D'occasion
EUR 85,48
Expédition à EUR 9,95
Expédition depuis Allemagne vers Etats-Unis
Expédition depuis Allemagne vers Etats-Unis
Quantité disponible : 1 disponible(s)
Image fournie par le vendeur
Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data (Springer Tracts in Natural Philosophy)
Edité par
Springer, New York, 1987
ISBN 10 : 0387965505
ISBN 13 : 9780387965505
Ancien ou d'occasion
Couverture rigide
Edition originale
Vendeur : Arroyo Seco Books, Pasadena, Member IOBA, Pasadena, CA, Etats-Unis
Évaluation du vendeur 4 sur 5 étoiles
Hardcover. Etat : Fine. 1st Edition. 191 Pp. Yellow Boards Stamped In Black. First Printing. Fine With Slight Fading To Yellow Cover On Spine. N° de réf. du vendeur 037300
Acheter D'occasion
EUR 93,24
Expédition à EUR 7,03
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 1 disponible(s)
Image d'archives
Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data. (= Springer tracts in natural philosophy, Volume 31). Tullio Valent Fundamental Structure.- 1.2. Special Subsets.- 1.3. Operators.- 1.4. Functionals.- §2. The Spectrum of an Operator.- 2.0. Preliminary Remarks.- 2.1. Basic Definitions.- 2.2. Functions of an Operator.- 2.3. Connection Between the Spectra of an Operator and its Inverse.- §3. Special Classes of Operators.- 3.0. Preliminary Remarks.- 3.1. CC Operator s. Definition and Basic Properties.- 3.2. CC Operators. Fredholm-Riesz Theory.- 3.3. Selfadjoint CC Operators.- 3.4. Selfadjoint, Normal, and Unitary Operators.- 3.5. Some Additional Conventions.- II. Function Spaces and Operators Generated by Differentiation.- §0. Introductory Remarks.- §1. The Space IH(F).- §2. Differential Operations and the Maximal Operator.- §3. The Minimal Operator and Proper Operators.- 3.1. The Minimal Operator.- 3.2. Transposed Opera
Edité par
Springer, New York, 1988
ISBN 10 : 0387965505
ISBN 13 : 9780387965505
Ancien ou d'occasion
Couverture rigide
Vendeur : BUCHSERVICE / ANTIQUARIAT Lars Lutzer, Wahlstedt, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
Hardcover. Etat : gut. 1988. Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which the boundary conditions are chosen, i.e. on the supplementary requirements which the solution is to satisfy on specified parts of the boundary. The branch of mathematical analysis dealing with the study of boundary value problems for partial differential equations is often called mathematical physics. Classical courses in this subject usually consider quite restricted classes of equations, for which the problems have an immediate physical context, or generalizations of such problems. With the expanding domain of application of mathematical methods at the present time, there often arise problems connected with the study of partial differential equations that do not belong to any of the classical types. The elucidation of the correct formulation of these problems and the study of the specific properties of the solutions of similar equations are closely related to the study of questions of a general nature. Detailangaben zum Buch - Partial Differential Equations: An Introduction to a General Theory of Linear Boundary Value Problems (Springer Series in Soviet Mathematics) EAN (ISBN-13): 9783540166993 ISBN (ISBN-10): 3540166998 Herausgeber: Springer ISBN/EAN: 3540166998 ISBN: 3-540-16699-8, 978-3-540-16699-3 Autor des Buches: boas Titel des Buches: partial differential equations boundary value problems, introduction the theory differential equations, linear theory, springer mathematics, general problems Autor/in: Aleksei A. Dezin Titel: Springer Series in Soviet Mathematics; Partial Differential Equations - An Introduction to a General Theory of Linear Boundary Value Problems Verlag: Springer; Springer Berlin 165 Seiten Erscheinungsjahr: 1987 Berlin; Heidelberg; DE Übersetzer/in: Ralph P. Boas (Russisch) Mathematik Analysis; Mathematische Analysis, allgemein; Verstehen; differential equation; partial differential equation; Boundary value problem; mathematical analysis; C; Analysis; Mathematics and Statistics I. Elements of Spectral Theory.- §0. Introductory Remarks.- §1. Basic Definitions.- 1.0. Introductory Remarks.- 1.1. Fundamental Structure.- 1.2. Special Subsets.- 1.3. Operators.- 1.4. Functionals.- §2. The Spectrum of an Operator.- 2.0. Preliminary Remarks.- 2.1. Basic Definitions.- 2.2. Functions of an Operator.- 2.3. Connection Between the Spectra of an Operator and its Inverse.- §3. Special Classes of Operators.- 3.0. Preliminary Remarks.- 3.1. CC Operator s. Definition and Basic Properties.- 3.2. CC Operators. Fredholm-Riesz Theory.- 3.3. Selfadjoint CC Operators.- 3.4. Selfadjoint, Normal, and Unitary Operators.- 3.5. Some Additional Conventions.- II. Function Spaces and Operators Generated by Differentiation.- §0. Introductory Remarks.- §1. The Space IH(F).- §2. Differential Operations and the Maximal Operator.- §3. The Minimal Operator and Proper Operators.- 3.1. The Minimal Operator.- 3.2. Transposed Operations and Adjoint Operators.- 3.3. Existence of Proper Operators.- §4. Weak and Strong Extensions of Differential Operations.- 4.0. Preliminary Remarks.- 4.1. Basic Definitions.- §5. Averaging Operators.- 5.0. Preliminary Remarks.- 5.1. Averaging on the Line.- 5.2. Averaging in a Multidimensional Domain.- 5.3. Averaging and the Differentiation Operation.- 5.4. The Friedrichs Lemma.- §6. The Identity of Weak and Strong Extensions of Differential Operations.- 6.1. The Case of Mainly Constant Coefficients.- 6.2. The Case of Variable Coefficients.- 6.3. Some Examples.- 6.4. Equivalence of Weak and Strong Extensions as a Corollary of the Unique Solvability Problems.- 6.5. The Case of an Ordinary Differential Operator.- §7. W Spaces.- 7.0. Introductory Remarks.- 7.1. Weak and Strong Generalized Derivatives.- 7.2. Spaces Wn\\ Wm, and Embedding Theorems.- III. Ordinary Differential Operators.- §0. Introductory Remarks.- §1. Description of Proper Operators for n = 1.- 1.1. Operators Generated by Cauchy Conditions.- 1.2. Description of Proper Operators.- §2. The Ordinary Differential Operator of the First Order.- §3. Birkhoff Theory.- §4. Supplementary Remarks.- 4.1. General Remarks.- 4.2. Supplementary Remarks Concerning Ordinary Differential Operations.- IV. Model Operators.- §0. Introductory Remarks.- §1. Tensor Products and Model Operators.- 1.1. Tensor Products of Hilbert Spaces.- 1.2. Model Operators.- §2. Operators on the n-Dimensional Torus.- 2.1. Definition of /7-Operators and their Basic Properties.- 2.2. Some Further Properties of 17-Operators.- 2.3. il-Operators Generated by Some Classical Differential Operations.- V. First-Order Operator Equations.- §0. Introductory Remarks.- §1. The Operator DtA; The Spectrum.- §2. The Operator Dt2013A; Special Boundary Conditions.- §3. The Operator Dtk\\Classification.- §4. Operators not Solvable for Dt.- §5. Differential Properties of the Solutions of Operator Equations, and Related Questions.- 6. Some Operators with Variable Coefficients in the Principal Part.- 7. Concluding Remarks.- VI. Operator Equations of Higher Order.- §0. Introductory Remarks.- §1. Second-Order Operator Equations.- 1.0. Preparatory Remarks.- 1.1. Elementary Formulas.- 1.2. A General Method.- 1.3. The Cauchy Problem.- 1.4. Existence of Proper Operators.- 1.5. The Dirichlet Problem.- 1.6. Using the Standard Conditions.- 1.7. A Concluding Remark.- §2. Operator Equations of Higher Order (m 2).- 2.0. Preparatory Remarks.- 2.1. Binomial Equations.- 2.2. The General Operator Equation.- VII. General Existence Theorems for Proper Operators.- §0. Introductory Remarks.- §1. Lemma on Restriction of a Domain.- §2. Existence Theorem for a Proper Operator.- 3. Description of Proper Operators in a Parallelepiped.- 3.0. Preparato. N° de réf. du vendeur BN133041
Acheter D'occasion
EUR 189,90
Expédition à EUR 39,95
Expédition depuis Allemagne vers Etats-Unis
Expédition depuis Allemagne vers Etats-Unis
Quantité disponible : 1 disponible(s)