Overview
This work presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials. The structure of conservation laws and new ideas and methods of constructing mathematical models are presented. The book presents an approach to the formalization of equations of continuum mechanics, in particular, relationships between the structure of thermodynamical conservation laws and representations of the rotation group. It describes the theory developed by Godunov together with his former student Evgenii Romenskii, which presents a systematization of different models of elastic media and related classification of hyperbolic equations.
Full Product Details
Author: S.K. Godunov ,
Evgenii I. Romenskii
Publisher: Springer Science+Business Media
Imprint: Kluwer Academic/Plenum Publishers
Edition: 2003 ed.
Dimensions:
Width: 15.50cm
, Height: 1.80cm
, Length: 23.50cm
Weight: 1.250kg
ISBN: 9780306477355
ISBN 10: 0306477351
Pages: 258
Publication Date: 31 May 2003
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
From the reviews: The authors present a systematic investigation of a variety of models in mathematical physics. ... The theory presented here stems from some very beautiful results obtained by the authors concerning the formulation of differential equations describing explosive deformations of metals. (Konstantina Trivisa, Mathematical Reviews, 2005 e)
From the reviews: <p> The authors present a systematic investigation of a variety of models in mathematical physics. a ] The theory presented here stems from some very beautiful results obtained by the authors concerning the formulation of differential equations describing explosive deformations of metals. (Konstantina Trivisa, Mathematical Reviews, 2005 e)
From the reviews: The authors present a systematic investigation of a variety of models in mathematical physics. ! The theory presented here stems from some very beautiful results obtained by the authors concerning the formulation of differential equations describing explosive deformations of metals. (Konstantina Trivisa, Mathematical Reviews, 2005 e)
