Operatorhalbgruppen und Evolutionsgleichungen/Operator Semigroups and Evolution Equations

Operatorhalbgruppen und Evolutionsgleichungen/Operator Semigroups and
Evolution Equations

Semester
WiSe 2018 / 19

Lecturer
Helmut Abels

Type of course (Veranstaltungsart)
Vorlesung

Contents
We will give an introduction to the theory of strongly continuous semigroups, which can be used to solve abstract evolution equations of the form

u'(t)+Au(t)= f(t)

and nonlinear variants. Here A is a suitable (unbounded) linear operator on a Banach space X and the equation can be seen as a Banach space valued ordinary differential equation. A lot of equation can be reformulated in this form, e.g. parabolic and hyperbolic partial differential equations and also equations from stochastic analysis. We will give a basic introduction to this theory and treat several applications, e.g. to the Navier-Stokes and Schrödinger equations.

Literature
M. Renardy und R. C. Rogers: An Introduction to Partial Differential Equations, Springer, 1993 (chapter 11)
A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983
A. Lunardi: Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkh"auser, 1995

Recommended previous knowledge
Analysis I-II, Lineare Algebra I-II, basic knowledge in measure and integration theory and functional analysis; basic knowledge in partial differential equations is not needed, but helpful.

Time/Date
Friday, 8-10

Location
M103

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=34222
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration

Registration for the exercise classes: via GRIPS/course homepage: Details will be given during
first week of lecture time. The exercise classes will take place every second week
("14-tägig", one hour of exercise classes).
Registration for course work/examination/ECTS: FlexNow

Course work (Studienleistungen)

Successful participation in the exercise classes: 50% of the maximal points of the solutions of
the exercise sheets; presentation of one solution
For module MV (without mark, "unbenotet"): passing a short oral examination
("Fachgespräch", 15 min.) on the content of the lecture series.

Examination (Prüfungsleistungen)

Oral exam: Duration: 20 minutes, Date: individual, re-exam: Date: individual

Regelungen bei Studienbeginn vor WS 2015 / 16

Benotet:
- O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
Unbenotet:
- O. g. Studienleistung und Bestehen der o. g. Prüfungsleistung

Modules
BV, MV, MAngAn

ECTS
4.5

Druckansicht