Bitte melden Sie sich über das Moodle-Portal für die Veranstaltung an. Die Vorlesungen und Übungen finden dieses Semester ausschließlich online über Moodle statt.
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.
Auf Wunsch der Teilnehmenden wird die Vorlesung auf Englisch gehalten.
This course will be taught in English.
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 during a weekly Zoom-session. The Zoom-session is scheduled for Friday: 12 - 2pm. Written solutions will be uploaded afterwards.
 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