by Steffen Härting
by Moritz Mercker
by Moritz Mercker
by Steffen Härting

Spaces of Radon Measures: Functional Analysis and Applications to PDEs

Structured population models are transport--type equations used to describe dynamics of populations with respect to a specific structural variable such as age, size or cell maturity. In this approach, the solution can be interpreted as a distribution of the population over possible values of the structural variable. This generality results in their wide applicability in demography, cell biology, immunology or ecology.
The goal of this lecture is the introduction of such equations in the setting of Radon measures over an abstract metric space (S,d) which is less restrictive for possible applications. To this end, profound knowledge on the functional analytic properties of the underlying measure space M(S) is needed and will be provided in the first part of the lecture.

Prerequisites: A basic course on functional analysis is required; Knowledge on measure theory and weak partial differential equations will be helpful but not necessary.

The lecture will cover the following topics:
  • Basics on Lipschitz functions and Functional Analysis: Norms for Lipschitz functions, approximations, proper metric spaces
  • Basics on Measure Theory: signed measures, narrow convergence, tightness, total variation norm
  • Properties of M(S) and the cone M+(S): introduction of the flat norm, separability, completeness, (local) compactness results
  • Structured Population Models on R+: existence, uniqueness, dependence on model functions, numerical algorithms
  • Structured Population Model on a general proper space
Lecturer: Professor Dr. Anna Marciniak-Czochra
Head Assistant: Christian Düll
Time: Tuesday, Thursday 9:30-11:00 (INF 205, SR B)
Tutorial: Monday 14.15-15.45 (INF 205, SR 5)
Please register via Müsli to the lecture. Any lecture material will be uploaded to Mampf.
  • C. Düll, P. Gwiazda, A.Marciniak-Czochra and J. Skrzeczkowski: Spaces of Measures and their Applications to Structured Population Models
  • A. Klenke: Probability Theory
  • P. Billingsley: Probability and Measure
  • H.W. Alt: Linear Functional Analysis
  • V.I. Bogachev: Measure Theory Vol I and II
  • R.M. Dudley: Real Analysis and Probability