Department of Mathematical Sciences

Dr Karsten Matthies

University of Bath


Contact

Department of Mathematical Sciences

Room Number:4 West 4.9
Telephone:+44 1225 383858
Internal Number:3858
Email:K.Matthies AT maths.bath.ac.uk
Postal Address:University of Bath
Department of Mathematical Sciences,
Bath,
BA2 7AY,
United Kingdom

Analysis Seminar


Teaching in 2014/15


Research interests

I am interested in supervising final year, MSc and PhD projects on the rigorous mathematical analysis of differential equations which are related to my research interests above. (Get in touch for further information.)

Some Activities:


Graduate Students

Adam Boden (2008-12) Travelling Waves in Heterogeneous Media

George Stone (2013- )


Preprints and Publications

Adam Boden, Karsten Matthies
Existence and Homogenisation of Travelling Waves Bifurcating from Resonances of Reaction-Diffusion Equations in Periodic media
Journal of Dynamics and Differential Equations, to appear. (preprint pdf)
Michael Herrmann, Karsten Matthies, Hartmut Schwetlick , Johannes Zimmer
Subsonic phase transition waves in bistable lattice models with small spinodal region
SIAM J. Math. Anal. 45 (2013), 26252645. (arxiv preprint), (journal artcile)
Amit Das, Amit Acharya , Johannes Zimmer , Karsten Matthies
Can equations of equilibrium predict all physical equilibria? A case study from Field Dislocation Mechanics
Mathematics and Mechanics of Solids 18 (2013), 803-822. (preprint pdf)
Karsten Matthies, Florian Theil
A semigroup approach to the justification of kinetic theory
SIAM J. Math. Anal. 44 (2012), 4345-4379. (journal article)
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. (journal article)
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.(preprint pdf)
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. (preprint pdf)
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
see also the Bath Online Publications Store OPUS , Google Scholar , and researcherid .

Last modified 01/09/2014