Dr Karsten Matthies

Contact

Department of Mathematical Sciences

Teaching

• Analysis 2b MA 20219

Research interests

• Averaging and Homogenisation for PDE
• Infinite-dimensional dynamics: PDEs and lattice ODEs
• Many particle dynamics
• Exponentially small effects

Activities:

• EPSRC Network: Mathematical Challenges of Molecular Dynamics
• Probability Laboratory at Bath

Preprints and Publications

Karsten Matthies, Florian Theil

A Semigroup Approach to the Justification of Kinetic Theory
submitted (preprint pdf)

Amit Acharya , Karsten Matthies, Johannes Zimmer

Travelling wave solutions for a quasilinear model of Field Dislocation Mechanics
Journal of the Mechanics and Physics of Solids 58 (2010), 2043-2053. (preprint pdf)

Karsten Matthies, Florian Theil

Validity and failure of the Boltzmann approximation of kinetic annihilation
Journal of Nonlinear Science 20 (2010), 1-46. (preprint pdf)

Christian Pfrang, Karsten Matthies

Small planar traveling waves in two dimensional networks of coupled oscillators
Dynamical Systems 24 (2009), 157-170. (preprint pdf).

Karsten Matthies, Florian Theil

Validity and and non-validity of propagation of chaos
in Analysis and Stochastics of Growth Processes and Interface Models (Edited by Peter Mörters, Roger Moser, Mathew Penrose, Hartmut Schwetlick, and Johannes Zimmer), OUP, 2008, 101-119.

Karsten Matthies

Exponential Averaging under Rapid Quasiperiodic Forcing
Advances in Differential Equations 13 (2008), 427-456.   (preprint pdf)

Vladimir Kamotski, Karsten Matthies, Valery Smyshlyaev

Exponential homogenization of linear second order elliptic problems with periodic coefficients
SIAM J. Math. Anal. 38 (2007), 1565-1587.

Karsten Matthies, Guido Schneider , Hannes Uecker

Exponential averaging for traveling waves in rapidly varying periodic media
Math. Nachr. 280 (2007), 408-422. (preprint gzipped postscript)     (preprint pdf)

Karsten Matthies

Exponential Estimates in Averaging and Homogenisation
in A. Mielke, editor, Analysis, Modeling, and Simulation of Multiscale Problems. Springer, 2006, 1-19.

Karsten Matthies, C.Eugene Wayne

Wave Pinning in Strips
Proc.Roy. Soc. Edinburgh A. 136 (2006), 971-995.

Karsten Matthies

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

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, Arnd Scheel

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

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

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.

Gero Friesecke, Karsten Matthies

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

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.

Karsten Matthies

Time-Averaging of parabolic partial differential equations: exponential estimates
Doctoral Thesis, Freie Universität Berlin, 1999

Karsten Matthies

A subshift of finite type in the Bogdanov-Takens bifurcation with D₃ symmetry
Doc. Math. J. DMV 4(1999), 463 -485.

Karsten Matthies

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

Last modified 28/09/2011