Functional Analysis

Nonlinear PDEs II

Summer 2012

Lectures

Mondays and Thursdays 10-12, Room 1.008 (Endenicher Allee 60)
Prof. J. J. L. Velázquez

Classes

Wednesdays 14-16, Room 2.040 (Endenicher Allee 60)
M. Helmers, S. Guo

Office hours

By appointment.

Examination

An oral examination will be held on 16.07. and 18.07.2012 in Room 2.023 (Endenicher Allee). Please sign up for a time slot in Room 2.016.

Course synopsis

The course presents some of the main techniques available to study well-posedness and qualitative behaviour of nonlinear PDEs. General methods for proving existence, uniqueness, and properties of solutions are studied along with examples that provide insight into obtaining these general results as well as their limitations.

 

Programme

  • Elliptic problems: variational methods, variational inequalities;
  • Nonvariational methods for elliptic and parabolic problems: weak solutions, regularity, viscosity solutions, bifurcation theory;
  • Second order hyperbolic equations.

Literature

  • L. C. Evans. Partial Differential Equations. Graduate Studies in Mathematics vol. 19, American Mathematical Society, 1991.
  • D. Gilbarg, N. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, 1977.
  • D. Henry. Geometric theory of seminlinear parabolic equations. Lecture Notes in Mathematics vol. 840, Springer-Verlag, 1981.
  • J. Smoller. Shock Waves and Reaction-Diffusion Equations. Grundlehren der mathematischen Wissenschaften vol. 258, Springer-Verlag, 1982.
  • G. B. Whitham. Linear and Nonlinear Waves. John Wiley & Sons, 1974.

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