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 bath.ac.uk
Postal Address:	University of Bath
	Department of Mathematical Sciences,
	Bath,
	BA2 7AY,
	United Kingdom

Teaching in 2024/25

MA40045 Dynamical Systems
MA40057 Functional Analysis

Research interests

Infinite-dimensional dynamics: PDEs and lattice ODEs
Many particle dynamics and their connections to kinetic equations
Averaging and Homogenisation for PDE
Exponentially small effects

Activities

I am member of the Analysis group and I am associated with the Probability Laboratory at Bath and the Centre for Nonlinear Mechanics (CNM) .
Member of KineticNet , funded by an INI network support grant.
Co-I of EPSRC network Generalised and Low-Regularity Solutions of Nonlinear PDEs for 2021-2024.
I co-organise. within the network a conference Analysis of PDEs in Mathematical Physics in June 2024
I co-organised within the network a conference Singularities and patterns in evolution equations in September 2023
Long-term stay at Frontiers in kinetic theory at the Isaac Newton Institute in 2022.

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 03/December/2024