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Elements of Continuum Mechanics and Conservation Laws
Rok: 2003
ISBN: 9780306477355
OKCZID: 110147980
Citace (dle ČSN ISO 690):
GODUNOV, Sergej Konstantinovič. Elements of continuum mechanics and conservation laws. Překlad Tamara ROZHKOVSKAYA. New York: Kluwer Academic/Plenum Publishers, c2003. viii, 258 s.
Anotace
Elements of Continuum Mechanics and Conservation Laws 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 final chapter: Structure of Thermodynamically Compatible Systems reflects Godunov's latest research. It 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. The material covered in this chapter was written during the preparation of the English edition and intensively discussed with specialists in different countries and presented at lectures given by Godunov in 2002. This book 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.