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Fortgeschrittene Themen der Differentialgleichungen (DGL IV) Nonlinear PDEs: Solutions and techniques

Fortgeschrittene Themen der Differentialgleichungen (DGL IV) Nonlinear PDEs: Solutions and techniques

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Some pdfs:

Exercises 1-5
Exercises 6-7

Exercises 1 - Solutions
Exercises 2 - Solutions
Exercises 3 - Solutions
Exercises 4 - Solutions
Exercises 5 - Solutions
Exercises 6 - Solutions
Exercises 7 - Solutions

Graph Riemann problem

 

Content:
These lectures focus on the theory of nonlinear PDEs with particular emphasis on hyperbolic and degenerate parabolic problems. The main focus is on different notions of a solution (with representative examples) and on corresponding methods and techniques for studying well-posedness.

Topics are:

  • Hyperbolic and degenerate parabolic PDEs,
  • Quasilinear and fully nonlinear PDEs,
  • Porous medium equation,
  • Reaction-diffusion systems,
  • Different types of solutions (variational, entropy, renormalized, kinetic, ...),
  • Well-posedness,
  • Typical solutions and explicit solutions,
  • Approximation of solutions,
  • Stability of solutions and singular limits,
  • Nonlinear analysis techniques for PDEs.

The lectures give 10 LP.
At the end of the lecture period there will be the possibility of oral examinations. 

Neue Räume! Das Gebäude MAR ist in der neue gelbe TU-Bau in der Marchstrasse, „hinter“ dem Mathegebäude auf der anderen Strassenseite der Marchstrasse.

Fortgeschrittene Themen der Differentialgleichungen (DGL IV)
Nonlinear PDEs: Solutions and techniques
Lectures
Wednesdays 12:00 - 14:00, Room: MA 648
Thursdays 10:00 - 12:00, Room: MAR 0.003
Boris Andreianov*
Exercise
Wednesdays 14:00 - 16:00, Room: MA 644
Thursdays 08:00 - 10:00, Room: MAR 0.003
Boris Andreianov*


Requirements:
Knowledge of fundamental ideas of calculus and functional analysis, classical functional spaces, concept of of weak solutions to PDEs.

Further information:
For further information, please, contact Dr. Christian Kreusler ().

Dr. hab. Boris Andreianov is Maître de Conférences at Université Franche-Comté in Besançon. During winter term 2013/2014 he is, BMS guest professor at TU Berlin.

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