# Items by Matthies, Dr Karsten

Up a level |

**21**.

## Book Sections

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

Boden, A. and Matthies, K., 2014. Forthcoming. Existence and Homogenisation of Travelling Waves Bifurcating from Resonances of Reaction-Diffusion Equations in Periodic Media. *Journal of Dynamics and Differential Equations*

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.