09224 - Continuum Mechanics

Learning outcomes

At the end of the course the students know some models of fluidodynamics, elasticity, and magnetofluidodynamics. He can understand and solve problems of stability and wave propagation, and acquires consciousness of the physical relevance of the problems dealt with.

Course contents

Introduction to partial differential equations: Cauchy problem, characteristics, classification and propagation of singularities. Short account of wave propagation theory, with examples. Riemann invariants. Tensor analysis. Introduction to continuum body: kinematics, dynamics and thermodynamics of fluids and elastic bodies. Balance equations and constitutive equations. Description of some mathematical models of fluids: barotropic ideal fluids and Navier-Stokes viscous fluids. Reynolds number. Existence of stationary classical solutions. Uniqueness and stability. The Navier model for elasticity. Gravitational instability and Jeans conditions. The model of perfect magnetofluidodynamics. Magneto-rotational instabilities. Shock waves: Euler's and Lundquist's models.

Readings/Bibliography

M.E. Gurtin An introduction to continuum mechanics, Academic Press 2003
F. John: Partial Differential Equations, Springer
B. Straughan: The energy method, stability and nonlinear convection, Springer 2007
M. Renardy, R.C. Rogers: An Introduction to Partial Differential Equations, Springer 2004
T. Ruggeri: Introduzione alla Termomeccanica dei Continui; Monduzzi 2007
E.R. Priest, T.G. Forbes: Magnetic Reconnection: MHD Theory and Applications; Cambridge University Press 2000
Lecture notes of the teacher

Teaching methods

The course consists of class-room lectures, where the basic elements of Continuum Mechanics are introduced, with a particular care for the mathematical models of Astrophysics.

Assessment methods

The assessmnet method consists in an oral exam which aims to assess the knowledge of the content of the course.

Office hours

See the website of Franca Franchi