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Workgroup Nonlinear Partial Differential Equations

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 3.029

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe
Germany

Office hours:
Mon-Fri 10-12, Tue+Wed 14-16

Tel.: +49 721 608 42064

Fax.: +49 721 608 46530

Nonlinear Maxwell equations — a variational approach (Summer Semester 2018)

Lecturer: Dr. Jaroslaw Mederski (Visiting.Professor)
Classes: Lecture (0154620)
Weekly hours: 2


Schedule
Lecture: Wednesday 11:30-13:00 Room 3.060 Build. 20.30 Begin: 9.5.2018
Thursday 9:45-11:15 Room 3.060 Build. 20.30
Please note the exact dates below!

Lecture dates:

WED May 9, 11:30-13:00
WED May 16, 11:30-13:00
THU May 24, 9:45-11:15
WED May 30, 11:30-13:00
WED June 6, 11:30-13:00
THU June 7, 9:45-11:15
WED June 13, 11:30-13:00
THU June 14, 9:45-11:15
WED June 20, 11:30-13:00
WED July 11, 11:30-13:00



All lectures will take place in room 3.060 (Build. 20.30).



Description of the lectures


Plan of the lectures

  • Nonlinear Dirichlet problem on a bounded domain. Mountain Pass Theorem and Nehari manifold approach.
  • General conditions imposed on the nonlinear term. Mountain Pass Theorem vs. Nehari manifold approach.
  • Functional and variational setting for the curl-curl equation on a bounded domain.
  • The role of the cylindrical symmetry in the curl-curl problems.
  • Generalized Nehari manifold approach for strongly indefinite problems. Critical point theory I.
  • Generalized Nehari manifold approach for strongly indefinite problems. Critical point theory II.
  • Ground state solutions and the multiplicity of bound state solutions.
  • Curl-curl equations in $\R^3$ and the lack of compactness.
  • Recent results and the list of open problems.





Lecture Notes, Nov. 15, 2018



Examination

There will be no examinations.