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Bifurcation Theory (Winter Semester 2022/23)

This lecture is intended to give an introduction to bifurcation theory with applications in ordinary and partial differential equations. It is suitable for students with knowledge covered by one of the lectures Functional analysis or Boundary and Eigenvalue Problems. The course is open to both Bachelor and Master students.

The first lecture is on Friday, October 28th, 2022.

Schedule
Lecture: Friday 9:45-11:15 SR 3.069 Begin: 28.10.2022, End: 13.2.2023
Problem class: Monday 9:45-11:15 SR 3.061 Begin: 31.10.2022, End: 13.2.2023
Lecturers
Lecturer PD Dr. Rainer Mandel
Office hours: by appointment
Room -1.019 Kollegiengebäude Mathematik (20.30)
Email: rainer.mandel@kit.edu
Problem classes M.Sc. Sebastian Ohrem
Office hours: Monday 14:00-15:30
Room 3.026 Kollegiengebäude Mathematik (20.30)
Email: sebastian.ohrem@kit.edu

The lecture will essentially deal with the Implicit Function Theorem (in Banach spaces), the Crandall-Rabinowitz Theorem and Hopf Bifurcation as well as their applications to Partial Differential Equations and Ordinary Differential Equations.

Problem Sheets

ProblemSheet01 Solutions01
ProblemSheet02 Solutions02
ProblemSheet03 Solutions03
ProblemSheet04 Solutions04 (Updated 9.1.23)
ProblemSheet05 Solutions05
ProblemSheet06 Solutions06
ProblemSheet07 Solutions07
ProblemSheet08 Solutions08
ProblemSheet09 Solutions09
ProblemSheet10 Solutions10
ProblemSheet11 Solutions11
ProblemSheet12

Addendum to the exercise session on 23.1.03

Examination

There will be oral exams.

References

  • Ambrosetti, Prodi: A Primer on Nonlinear Analysis
  • Ambrosetti, Malchiodi: Nonlinear analysis and semilinear elliptic problems
  • Chang: Methods in nonlinear analysis
  • Deimling: Nonlinear functional analysis (The Dover Books series)
  • Kielhöfer: Bifurcation Theory : An Introduction with Applications to Partial Differential Equations
  • Evans: Partial differential equations