**PDE and modelling** (V3B2/F4B1)

**Classes.**

Wednesday 10(c.t)-12 We10/Zeichensaal |

Friday 8.30(sharp, no break)-10 We10/Zeichensaal |

**Tutorials.**

R. Winter

There will be two tutorial groups.

Tuesday 16(c.t.)-18 SemR 0.007, C. Eichenberg

Wednesday 8(c.t.) -10 SemR 0.007, N. Lipski

**Exams.**

The exam will be oral.

The first session will be on Thursday 28 and Friday 29 July.

The second session on Wednesday 7 and Thursday 8 September.

All exams will take place in **Room 4.045.**

**Problem sheets.**

Problem sheets are handed out in the lecture on Fridays and are available below. Solutions may be submitted in groups of two students who attend the same tutorial and are collected on Fridays during the lecture.

Lecture notes (work in progress: lectures 1-24)

**Content.**

The course deals with the mathematical modeling of physical systems, and the analysis of the resulting partial differential equations.

The course will consist of three main parts:

- Continuum mechanics and modeling (in particular kinematics, balance laws, constitutive equations, and examples)
Fluid mechanics (in particular compressible and incompressible Euler and Navier-Stokes equations)

- Solid mechanics and elasticity (in particular direct and indirect methods of the calculus of variations, notions of convexity, nonlinear elasticity and its linearization)

Classes will be in English.

**Prerequisites.**

The contents of the lectures ”Introduction to PDE” and ”PDE and Functional Analysis” are presumed to be known. In particular, properties of Sobolev spaces and weak convergence will be used. A basic physics background is helpful but not required.

To catch up with the necessary background we recommend

- H. Brezis, Functional Analysis, Sobolev spaces and partial differential equations, Springer 2010 • L.C. Evans, Partial Differential Equations, American Math. Soc. 1998
L.C. Evans, Partial Differential Equations, American Math. Soc. 1998