Dr. Karsten Matthies

New web-page in Bath

Old web-page until August 2005:

Old Projects

• Quantitative homogenization and averaging
  (DFG Priority Research Program 1095 on Analysis, modeling, and simulation of multiscale problems)

Old Teaching

• Seminar Wintersemester 2004/05: Unendlichdimensionale Dynamik
• Vorlesung Sommersemester 2004: Partielle Differentialgleichungen II
• Vorlesung Wintersemester 2003/04: Partielle Differentialgleichungen I
• Vorlesung Sommersemester 2003: Dynamische Systeme II
• Vorlesung Wintersemester 2002/03: Dynamische Systeme I

Preprints and Publications (updated until Aug 2005)

Karsten Matthies

The Bogdanov-Takens Bifurcation implies Chaos in Dynamical Systems with D₃ Symmetry
Diplomarbeit, 1996

Karsten Matthies

A subshift of finite type in the Bogdanov-Takens bifurcation with D_{3} symmetry
Doc. Math. J. DMV 4(1999), 463 -485.

Karsten Matthies

Time-Averaging of parabolic partial differential equations: exponential estimates
Dissertation FU Berlin, 1999

Karsten Matthies

Time-Averaging under Fast Periodic Forcing of Parabolic Partial Differential Equations: Exponential Estimates
Journal of Differential Equations 174 (2001), 133-180.
Short version in Proceedings of Equadiff 99, B. Fiedler, K. Gröger, and J. Sprekels (eds.), World Scientific Publishing, Singapore (2000), 952-954.

Gero Friesecke, Karsten Matthies

Atomic-scale localization of high-energy solitary waves on lattices
Physica D 171 (2002), 211-220.

Karsten Matthies

Backward error analysis of a full discretisation scheme for a class of parabolic partial differential equations
Nonlinear Anal. Theory Methods Appl. 52 (2003), 805-826.

Karsten Matthies

Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing
Discrete Contin. Dyn. Syst. 9 (2003), 585-602.

Karsten Matthies, Arnd Scheel

Exponential Averaging of Hamiltonian Evolution Equations
Trans. Amer. Math. Soc. 355 (2003), 747-773.

Gero Friesecke, Karsten Matthies

Geometric solitary waves in a 2D mass-spring lattice
Discrete Contin. Dyn. Syst. Ser. B 3 (2003), 105-114.

Karsten Matthies

Homogenisation of Exponential Order for Elliptic Systems in Infinite Cylinders
Asymptot. Anal. 43 (2005), 205-232.

Karsten Matthies

Exponential Averaging of Rapid Quasiperiodic Forcing
Preprint no 88, Schwerpunkt Multiscale Problems.

Karsten Matthies, C.E. Wayne

Wave Pinning in Strips
Preprint no 142, Schwerpunkt Multiscale Problems.

Karsten Matthies, Guido Schneider, Hannes Uecker

Exponential averaging and traveling waves in rapidly varying periodic media
Preprint no 158, Schwerpunkt Multiscale Problems (2004).
(gziped postscript)     (pdf)