# 101.820 AKNUM Non-local operators This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2019W

2019W, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture

## Learning outcomes

After successful completion of the course, students are able to understand operator equations with non local operators analytically and numerically.

Especially students learn to cope with integral equations and the fractional Laplacian.

## Subject of course

This lecture deals with non-local operators. Classical examples are integral operators with singular kernel (of convolution type) that arise from reformulations of PDEs as integral equations. We will at first study some analytic properties of these operators (e.g. mapping properties in Sobolev spaces) and afterwards discuss numerical methods (the boundary element method) for these equations as well as their advantages and disadvantages.

As a second model example of a non-local operator, we consider the fractional Laplacian, which is a non-integer power of the classical Laplacian. Such operators appear naturally in more refined models of anomalous diffusion in physics, biology or finance. Mathematically, there are various definition of the fractional Laplacian, which are not equivalent on bounded domains. In this lecture, we will consider two different definitions - the spectral and integral fractional Laplacian - and discuss numerical methods for these two definitions.

## Teaching methods

Lecture on the blackboard

Oral

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 15:3010.10.2019Sem.R. DA grün 03 B Vorbesprechung / Einführende Vorlesung
Tue13:00 - 14:0015.10.2019 - 28.01.2020 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu15:00 - 16:0017.10.2019 - 31.10.2019 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu15:00 - 16:0007.11.2019Sem.R. DC rot 07 AKNUM Nichtlineare Operatoren
Thu15:00 - 16:0014.11.2019 - 30.01.2020 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
AKNUM Non-local operators - Single appointments
DayDateTimeLocationDescription
Thu10.10.201914:00 - 15:30Sem.R. DA grün 03 B Vorbesprechung / Einführende Vorlesung
Tue15.10.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu17.10.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue29.10.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu31.10.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue05.11.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu07.11.201915:00 - 16:00Sem.R. DC rot 07 AKNUM Nichtlineare Operatoren
Tue12.11.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu14.11.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu21.11.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue26.11.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu28.11.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue03.12.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu05.12.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue10.12.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu12.12.201915:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue17.12.201913:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue07.01.202013:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Thu09.01.202015:00 - 16:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren
Tue14.01.202013:00 - 14:00 Sem.R. DA grün 03CAKNUM Nichtlineare Operatoren

## Examination modalities

Oral examination, make an appointment via e-mail

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Mandatory elective

## Literature

Lecture notes are created parallel to the course.

German