Partial Differential Equations
This course is offered in the summer semester 2023. Lectures are on Thursdays, 10.15 am and on Fridays, 12.15 am. The lecture will be held in English. Please register in Moodle for the lecture. The material for the course and the exercises will be available only at the moodle page of the course.
Content of the lecture
Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena arising in various fields of science such as heat conduction, elasticity, electrodynamics, fluid flow, chemical reaction, quantum mechanics or Black-Scholes option pricing model in mathematical finance... Study on PDEs therefore plays an important role in applications concerning many different fields and motivates researcher all over the world.
The aim of this course is to give an introduction to the theory of PDEs. We first learn what partial differential equations are and give a classification. Then, we will study three important class of PDEs: elliptic, parabolic and hyperbolic PDES. We will study: existence, uniqueness and qualitative properties of solutions both in a classical and in a weak setting. We will mainly concentrates on linear equations.
The exercises are very important to understand the contents of the lecture. There will be a weekly exercise sheet which will be discussed in the weekly exercise classes on Wednesdays, 8.15 am.
- 9 ECTS
- 4+2 hours
 L. Evans, Partial Differential Equations, American Mathematical Society
 M. Renardy, R. Rogers, An Introduction to Partial Differential Equations, Springer
 F. Sauvigny, Partielle Differentialgleichungen der Geometrie und der Physik, Springer
 B. Schweizer, Partielle Differentialgleichungen, Springer