Boundary value problems of finite elasticity : local theorems on existence, uniqueness, and analytic dependence on data / Tullio Valent

• Autore: Valent, Tullio
• Pubblicazione: New York, : Springer, 1988
• Titolo uniforme: Boundary value problems of finite elasticity
• Descrizione fisica: xii, 191 p. ; 25 cm
• Soggetto topico: 34Bxx - Boundary value problems for ordinary differential equations [MSC 2020]; 35B30 - Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs [MSC 2020]; 74-XX - Mechanics of deformable solids [MSC 2020]; 74B20 - Nonlinear elasticity [MSC 2020]
• Soggetto non controllato: Banach Spaces; Deformation; Development; Elasticity; Elastostatics; Implicit functions; Materials; Measure; Statics
• Nota di contenuto: 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 Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality.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.
• Titolo autorizzato: Boundary Value Problems of Finite Elasticity
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00269009
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: https://doi.org/10.1007/978-1-4612-3736-5
• Serie: Springer tracts in natural philosophy Berlin [etc.] . -Springer , 1964-1998. ; 31