#### Modeling PDEs

# Mathematical Modeling with PDEs

#### Info

The structure of the class will be 3 hours of lectures and 1 hour of tutorial each week.

Lecture times:

Tuesdays, 10:30 - 12:00, in 1090(Rogowski)|328

Thursdays, 12:30 - 14:00, in 1090(Rogowski)|328

Tutorials will be held roughly every other week instead of the lecture on Thursday.

There are 6 ECTS points to earn with an oral exam of 30min.

##### Planning of the lecture in view of the restrictions of public life

** [Status planning 25.3.2020]:** The lecture will start as planned on 7.4.2020 in a virtual form. The current state of planning is that the lectures and exercises will be streamed using the platform Zoom. Zoom allows an interactive form of the lectures and joining and interacting is strongly recommended. More information will follow here and on Moodle.

#### Intention

The class presents a cohesive mathematical derivation and discussion of different partial differential equations as models for technical and physical processes. Basic framework will be the balance laws of mass, momentum and energy, as well as the Maxwell equations. Different constitutive material laws will yield different models.

We will consider among others: solid mechanics, fluid and gas dynamics, chemical reactions, magnetohydrodynamics. As application examples we study models for rubber, earthquakes, flames, shock waves, electric arcs, etc.

The aim is to view the connections of relevant PDEs in applied mathematics and master the process of modelling from the physical concept the mathematical equation up to a concrete result.

#### Some Background Literature

This is not meant to cover the course, most of these books actually go far beyond the course material.
But the books certainly resonate with what is done in the course.

R. Temam, A. Miranville, Mathematical Modeling in Continuum Mechanics, Cambridge University Press, 2000

R. Greve, Kontinuumsmechanik, Springer, Berlin, 2003

H. Schade & K. Neemann, Tensoranalysis, DeGruyter, Berlin, 2009

I. Müller & P. Strehlow, Rubber and Rubber Balloons, Springer 2004

C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 3rd ed., Springer 2010

S. R. De Groot & P. Mazur, Irreversible Themrodynamics, Dover, 1962

A. Meister, Asymptotic single and multiple scale expansions in the low Mach number limit, SIAM J. Appl. Math 60/1, (1999)

S. Chapman & T. G. Cowling, The Mathematical Theory of Non-uniform Gases, 3rd ed., Cambridge University Press, 1970

F. Cap, Lehrbuch der Plasmaphysik und Magnetohydrodynamik, Springer, 1994