Mathematical modelling in continuum mechanics (Q2703184)

The book contains the fundamentals of continuum mechanics: description of motion of a continuous body, the laws of dynamics, Cauchy stress tensor, the constitutive laws, internal energy and the first principle of thermodynamics, shocks and Rankine-Hugoniot relations, an introduction to fluid mechanics for inviscid and viscous Newtonian fluids, and an introduction to linear elasticity and to variational principles in linear elasticity. It contains also more or less detailed introduction to several important related fields that could be themselves the subjects of separate books: magnetohydrodynamics, combustion, geophysical fluid dynamics, vibrations, linear acoustics, nonlinear waves and solitons in the context of Korteweg-de Vries and nonlinear Schrödinger equations. Correspondingly, the book consists of four main parts: fundamental concepts in continuum mechanics, physics of fluids, solid mechanics, and introduction to wave phenomena. Selected parts of this book are suitable for a one-semester course either on the fundamentals of continuum mechanics or a combination of selected topics. Especially effectively this book can be used in combination with other book of the first author [\textit{R. Temam}, Infinite-dimensional dynamical systems in mechanics and physics. 2nd ed. Applied Mathematical Sciences. 68. New York, NY: Springer. xxi (1997; Zbl 0871.35001)] devoted to mechanical and physical introduction to the theory of dynamical systems.