# Items by Matthies, Dr Karsten

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**25**.## Book Sections

Herrmann, M. and Matthies, K., 2017. Forthcoming. Uniqueness of solitary waves in the high-energy limit of FPU-type chains.

*In*:*Patterns of Dynamics Confererence.*Springer.Matthies, K. and Theil, F., 2008. Validity and and non-validity of propagation of chaos.

*In*: Mörter, P., Moser, R., Penrose, M., Schwetlick, H. and Zimmer, J., eds.*Analysis and Stochastics of Growth Processes and Interface Models.*Oxford, pp. 101-119.Matthies, K., 2006. Exponential estimates in averaging and homogenisation.

*In*:*Analysis, modeling and simulation of multiscale problems.*Berlin: Springer, 1--19.## Articles

Matthies, K., Stone, G. R. and Theil, F., 2017. The derivation of the linear Boltzmann equation from a Rayleigh gas particle model.

*Kinetic and Related Models*Item availability may be restricted.Matthies, K. and Uecker, H., 2016. Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media.

*Asymptotic Analysis*, 99 (1-2), pp. 53-65.Herrmann, M. and Matthies, K., 2015. Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains.

*Nonlinearity*, 28 (8), pp. 2767-2789.Boden, A. and Matthies, K., 2014. Existence and homogenisation of travelling waves bifurcating from resonances of reaction-diffusion equations in periodic media.

*Journal of Dynamics and Differential Equations*, 26 (3), pp. 405-459.Das, A., Acharya, A., Zimmer, J. and Matthies, K., 2013. Can equations of equilibrium predict all physical equilibria? A case study from Field Dislocation Mechanics.

*Mathematics and Mechanics of Solids*, 18 (8), pp. 803-822.Herrmann, M., Matthies, K., Schwetlick, H. and Zimmer, J., 2013. Subsonic phase transition waves in bistable lattice models with small spinodal region.

*SIAM Journal on Mathematical Analysis (SIMA)*, 45 (5), pp. 2625-2645.Matthies, K. and Theil, F., 2012. A semigroup approach to the justification of kinetic theory.

*SIAM Journal on Mathematical Analysis (SIMA)*, 44 (6), 4345–4379.Acharya, A., Matthies, K. and Zimmer, J., 2010. Travelling wave solutions for a quasilinear model of field dislocation mechanics.

*Journal of the Mechanics and Physics of Solids*, 58 (12), pp. 2043-2053.Matthies, K. and Theil, F., 2010. Validity and failure of the Boltzmann approximation of kinetic annihilation.

*Journal of Nonlinear Science*, 20 (1), pp. 1-46.Pfrang, C. and Matthies, K., 2009. Small planar travelling waves in two-dimensional networks of coupled oscillators.

*Dynamical Systems: An International Journal*, 24 (2), pp. 157-170.Matthies, K., 2008. Exponential averaging under rapid quasiperiodic forcing.

*Advances in Differential Equations*, 13 (5-6), pp. 427-456.Kamotski, V., Matthies, K. and Smyshlyaev, V. P., 2007. Exponential homogenization of linear second order elliptic PDEs with periodic coefficients.

*SIAM Journal on Mathematical Analysis (SIMA)*, 38 (5), pp. 1565-1587.Matthies, K., Schneider, G. and Uecker, H., 2007. Exponential averaging for traveling wave solutions in rapidly varying periodic media.

*Mathematische Nachrichten*, 280 (4), pp. 408-422.Matthies, K. and Wayne, C. E., 2006. Wave pinning in strips.

*Proceedings of the Royal Society of Edinburgh Section A - Mathematics*, 136 (5), pp. 971-995.Matthies, K., 2005. Homogenisation of exponential order for elliptic systems in infinite cylinders.

*Asymptotic Analysis*, 43 (3), pp. 205-232.Matthies, K., 2003. Backward error analysis of a full discretization scheme for a class of semilinear parabolic partial differential equations.

*Nonlinear Analysis: Theory Methods & Applications*, 52 (3), pp. 805-826.Friesecke, G. and Matthies, K., 2003. Geometric solitary waves in a 2D mass-spring lattice.

*Discrete and Continuous Dynamical Systems - Series B*, 3 (1), pp. 105-144.Matthies, K. and Scheel, A., 2003. Exponential averaging for Hamiltonian evolution equations.

*Transactions of the American Mathematical Society*, 355 (2), pp. 747-773.Matthies, K., 2003. Exponentially small splitting of homoclinic orbits of parabolic differential equations under periodic forcing.

*Discrete and Continuous Dynamical Systems*, 9 (3), pp. 585-602.Friesecke, G. and Matthies, K., 2002. Atomic-scale localization of high-energy solitary waves on lattices.

*Physica D: Nonlinear Phenomena*, 171 (4), pp. 211-220.Matthies, K., 2001. Time-averaging under fast periodic forcing of parabolic partial differential equations: exponential estimates.

*Journal of Differential Equations*, 174 (1), pp. 133-180.Matthies, K., 1999. A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry.

*Documenta Mathematica*, 4, pp. 463-485.