Partial Differential Equations

Content

This course, together with the course Functional Analysis, forms the basis of the studies in the area of analysis in the master programme.

A wide variety of mathematical models can be formulated in terms of a partial differential equation (PDE). For example, PDEs are used to describe phenomena such as diffusion, heat conduction, elasticity, electrodynamics, fluid flow and quantum mechanics. They also play an important role in mathematical finance, e.g. in the Black-Scholes option pricing model.

The course gives an introduction to the theory of PDEs. We will study the prototypes of the three basic types of PDEs encountered in many applications (elliptic, parabolic and hyperbolic equations) and discuss several notions of solution. We will also make use of functional analytic methods. The basic concepts needed in this respect will be recalled.

Prerequisites

Analysis I, II
Measure Theory
basic knowledge in functional analysis would be desirable

Examination

oral exam

Recommended literature

L. Evans: Partial Differential Equations, American Mathematical Society
B. Schweizer: Partielle Differentialgleichungen: Eine anwendungsorientierte Einführung, Springer
M. Renardy, R. Rogers: An Introduction to Partial Differential Equations, Springer
F. Sauvigny, Partielle Differentialgleichungen der Geometrie und der Physik, Springer
J. Jost, Partielle Differentialgleichungen, Springer
S. Salsa: Partial Differential Equations in Action, Springer

The literature is here available.