Introductory Topics In The Mathematical Theory （介绍数学理论的主题）.pdfVIP

CONTINUUM MECHANICS - Introductory Topics In The Mathematical Theory Of Continuum Mechanics - R J Knops and R. Quintanilla INTRODUCTORY TOPICS IN THE MATHEMATICAL THEORY OF CONTINUUM MECHANICS R J Knops School of Mathematical and Computer Sciences, Heriot-Watt University, UK R. Quintanilla Department of Applied Mathematics II, UPC Terrassa, Spain Keywords: Classical and non-classical continuum thermomechanics, well- and ill- posedness; non-linear, linear, linearized, initial and boundary value problems, existence, uniqueness, dynamic and spatial stability, continuous data dependence. Contents S S I. GENERAL PRINCIPLES S 1. Introduction L R 2. The well-posed problem II. BASIC CONTINUUM MECHANICS O E 3. Introduction T 4. Material description E 5. Spatial description P 6. Constitutive theories – III. EXAMPLE: HEAT CONDUCTION A 7. Introduction. Existence and uniqueness H O 8. Continuous dependence. Stability 9. Backward heat equation. Ill-posed problems C C 10. Non-linear heat conduction 11. Infinite thermal wave speeds S E IV. CLASSICAL THEORIES E 12. Introduction L 13. Thermoviscous flow. Navier-Stokes Fluid N 14. Linearized and linear elastostatics P 15. Linearized Elastodynamics U 16. Linearized and linear thermoelastostatics M 17. Linearized and linear thermoelastodynamics A 18. Viscoelasticity 19. Non-linear Elasticity S 20. Non-linear thermoelasticity and thermoviscoelasticity V. NON-CLASSICAL THEORIES 21. Introduction 22. Isothermal models 23