Department of Mathematical Sciences

Dr Karsten Matthies

University of Bath


Department of Mathematical Sciences

Room Number:4 West 4.9
Telephone:+44 1225 383858
Internal Number:3858
Email:k.matthies AT
Postal Address:University of Bath
Department of Mathematical Sciences,
BA2 7AY,
United Kingdom

Teaching in 2023/24

Research interests


Graduate Students

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

George Stone (2013-2017) Derivation of Kinetic Equations from Particle Models (thesis pdf).

Matthias Klar (2017-2021) [jointly with Johannes Zimmer] Scale-bridging of fast-slow systems in a thermodynamical setting (thesis pdf) funded by SAMBa.

Rosa Kowalewski (2020-) [jointly with David Tsang ] funded by SAMBa.

Theodora Syntaka (2020-) supported by a Leverhulme grant in collaboration with Florian Theil.

Jonty Sewell (2021-) [jointly with Miles Wheeler ]

Preprints and Publications

Karsten Matthies, Theodora Syntaka
Fractional diffusion as the limit of a short range potential Rayleigh gas
(arxiv preprint)
Karsten Matthies, Theodora Syntaka
Derivation of kinetic and diffusion equations from a hard-sphere Rayleigh gas using collision trees and semigroups
accepted as part of a volume LMS lecture notes (arxiv preprint)
Karsten Matthies, Johannes Nordström, Matthew Turner
SU(2)2xU(1)-invariant G2-instantons on the AC limit of the C7 family
accepted by Communications in Analysis and Geometry (arxiv preprint)
Karsten Matthies, Jonty Sewell, Miles Wheeler
Solitary solutions to the steady Euler equations with piecewise constant vorticity in a channel
Journal of Differential Equations 400, 376-422 (2024). (arxiv preprint)
Matthias Klar, Karsten Matthies, Johannes Zimmer
Second-order asymptotic expansion and thermodynamic interpretation of a fast–slow Hamiltonian system
Letters in Mathematical Physics, (2022) 112:119. (arxiv preprint)
Matthias Klar, Karsten Matthies, Celia Reina, Johannes Zimmer
Second-order fast-slow dynamics of non-ergodic Hamiltonian systems: Thermodynamic interpretation and simulation
Physica D, 428 (2021), article no 133036. (arxiv preprint)
Michael Herrmann, Karsten Matthies
A uniqueness result for a simple superlinear eigenvalue problem
Journal of Nonlinear Science 31, 27 (2021). (arxiv preprint)
Michael Herrmann, Karsten Matthies
Nonlinear and Nonlocal Eigenvalue Problems: variational existence, decay properties, approximation, and universal scaling limits
Nonlinearity 33 (2020), 4046-4074 (arxiv preprint)
Michael Herrmann, Karsten Matthies
Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains
Trans. Amer. Math. Soc. 372 (2019), 3425-3486. (arxiv preprint)
Karsten Matthies, Florian Theil
Rescaled Objective Solutions of Fokker-Planck and Boltzmann equations
SIAM J. Math. Anal. 51 (2019), 1321-1348. (arxiv preprint)
Michael Herrmann, Karsten Matthies
Solitary waves in atomic chains and peridynamical media
Mathematics in Engineering 1 (2019), 281-308.
(arxiv preprint)
Karsten Matthies, George Stone
Derivation of a Non-autonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas
Discrete Contin. Dyn. Syst. 38 (2018), 3299-3355 (arxiv preprint)
Karsten Matthies, George Stone, Florian Theil
The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle Model
Kinetic and Related Models 11 (2018), 137 - 177 (arxiv preprint) (local preprint pdf)
Michael Herrmann, Karsten Matthies
Uniqueness of solitary waves in the high-energy limit of FPU-type chains
In: Gurevich P., Hell J., Sandstede B., Scheel A. (eds) Patterns of Dynamics. PaDy 2016. Springer Proceedings in Mathematics & Statistics, vol 205, Springer, 2017, p.3-15. (arxiv preprint).
Karsten Matthies, Hannes Uecker
Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media
Asymptot. Anal. 99 (2016), 53-65. (preprint pdf)
Michael Herrmann, Karsten Matthies
Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains
Nonlinearity 28 (2015), 2767-2789. (arxiv preprint), (local copy).
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 26 (2014), 405-459. (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), 2625-2645. (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.
(published version pdf)
Karsten Matthies
Homogenisation of Exponential Order for Elliptic Systems in Infinite Cylinders
Asymptot. Anal. 43 (2005), 205-232.
(author accepted version pdf)
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. (published version pdf)
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. (author accepted version pdf)
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.
(author accepted version pdf)
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 my profiles on arXiv, Bath Research Portal, Google Scholar , orcid , researchgate .

Last modified 30/May/2024