Conservation Laws in Continuum Physics

Short Course Organizer
Constantine M. Dafermos, Brown University,

Associated SIAM Conference
SIAM Conference on Analysis of Partial Differential Equations

Classical continuum physics is the source of many noteworthy partial differential equations. In return, the theory of partial differential equations has been addressing questions raised by continuum physics. Despite this intimate relationship, continuum physics has been fading away from the curricula of US mathematics, and even applied mathematics, departments. The aim of the course is to alert young analysts to the benefits derived from familiarity with the elements of continuum physics, and to motivate them to study that field.

Constantine M. Dafermos, Professor of Applied Mathematics, Brown University.
Scientific interests: continuum mechanics and thermodynamics, nonlinear partial differential equations, especially hyperbolic systems of conservation laws.

Course Description
The course will provide a self-contained introduction to the structure of continuum theories. The presentation will be suitable for audiences with a certain mathematical sophistication but without any background in continuum physics. The course will explain how the classical nonlinear partial differential equations arise in the context of continuum physics, and in particular it will emphasize how the familiar dissipative mechanisms of viscosity, relaxation, etc. are induced by the laws of thermodynamics.

Level of the Material
The level of the course will proceed from beginner to intermediate. Of course, the hope is that the course will provide stimulation for further study.

Target Audience
Mathematicians and applied mathematicians with background and interest in nonlinear partial differential equations.

Recommended Background
Standard familiarity with the principles of analysis. Accessible to graduate students and beyond.
Course Outline
Notion of a "balance law". The balance laws of continuum physics. Entropy and the Second Law  of thermodynamics. Material models with elastic response or internal dissipation. Viscosity and relaxation mechanisms. Systematic derivation of the classical, nonlinear partial differential equations

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