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Topics in PDE: proposals
All participants in the courses Theory of differential equations and Partial differential
equations D, especially those taking the latter (6.0 hp) course, are invited to present orally
some chapter from the theory or applications of partial differential equations.
The proposal themes can be
downloaded
from Professor Crister Kiselman site.
You can chose the projects with numbers of themes as listed below:
NN: 16, 911, 13, 15, 17, 18, 23, 25, 29, 30, 35, 3839, 4142
You can additionally use the following themes:
 Chemotactic cell motion and biological pattern fomation
Review Chapter 4 of the book of P.A. Markowich,
Applied partial differential equations : a visual approac
Berlin, New York: Springer, 2007.
 Free boundary problems and phase transitions
Review Chapter 6 of the book of P.A. Markowich,
Applied partial differential equations : a visual approac
Berlin, New York: Springer, 2007.
 Digital image processing
Review Chapter 10 of the book of P.A. Markowich,
Applied partial differential equations : a visual approac
Berlin, New York: Springer, 2007.
 Sandpiles and river networks
Review the
article
by L. Prigozhin, Sandpiles and river networks: extended systems with nonlocal interactions.
Phys. Rev. E (3) 49 (1994), no. 2, 11611167.
Continuum model of sandpile growth with demonstration of instantaneous longrange interactions and sudden collapses typical of real sandpiles.

Particle trajectories in solitary water waves
Review the
article
by A. Constantin and J. Escher Particle trajectories in solitary water waves ,
Bull. Amer. Math. Soc. 44 (2007), 423431.

Mathematical methods in medical image processing
Review the
article
by S. Angenent, E. Pichon and A. Tannenbaum Mathematical methods in medical image processing
Bull. Amer. Math. Soc. 43 (2006), 365396.
The books are available from the
Uppsala univeristetsbibliotek
(you can also try the full search by
Bibliotek.se
).
Each group has 20 minutes for presentation. We can arrange presentations during the lectures starting from September 25. You need to inform me about
the planned time.
