Mathematical Modeling in Continuum Mechanics

Topics include: viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics and solitons.

Roger Temam (Author), Alain Miranville (Author)

9780521617239, Cambridge University Press

Paperback, published 19 May 2005

356 pages, 55 exercises
22.8 x 15.5 x 1.7 cm, 0.52 kg

'This second edition is a unique resource for physicists, applied mathematicians and engineers studying the general themes of fluid and solid mechanics. ... an ideal self-study vehicle for practicing physicists, applied mathematicians and engineers. Furthermore, it is an excellent introductory text for advanced engineering students and anyone interested in continuum mechanics.' Zentralblatt MATH

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Introduction
A few words about notations
Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics
2. The fundamental law of dynamics
3. The Cauchy stress tensor - applications
4. Real and virtual powers
5. Deformation tensor, deformation rate tensor, constitutive laws
6. Energy equations and shock equations
Part II. Physics of Fluids: 7. General properties of Newtonian fluids
8. Flows of inviscid fluids
9. Viscous fluids and thermohydraulics
10. Magnetohydrodynamics and inertial confinement of plasmas
11. Combustion
12. Equations of the atmosphere and of the ocean
Part III. Solid Mechanics: 13. The general equations of linear elasticity
14. Classical problems of elastostatics
15. Energy theorems - duality: variational formulations
16. Introduction to nonlinear constitutive laws and to homogenization
17. Nonlinear elasticity and an application to biomechanics
Part IV. Introduction to Wave Phenomena: 18. Linear wave equations in mechanics
19. The soliton equation: the Kortewed-de Vries equation
20. The nonlinear Schrödinger equation
Appendix
Hints for the exercises
References
Index.

Subject Areas: Nonlinear science [PBWR], Mathematical modelling [PBWH], Applied mathematics [PBW]