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Research Output

  • 27 Article
  • 2 Chapter
  • 1 Conference contribution
  • 1 Conference article
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2020

Nonlinear and Nonlocal Eigenvalue Problems: variational existence, decay properties, approximation, and universal scaling-

Herrmann, M. & Matthies, K., 25 Mar 2020, (Accepted/In press) In : Nonlinearity.

Research output: Contribution to journalArticle

2019

Rescaled Objective Solutions of Fokker-Planck and Boltzmann equations

Matthies, K. & Theil, F., 31 Dec 2019, In : SIAM Journal on Mathematical Analysis (SIMA). 51, 2, p. 1321–1348 28 p.

Research output: Contribution to journalArticle

Open Access
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76 Downloads (Pure)

Solitary waves in atomic chains and peridynamical media

Herrmann, M. & Matthies, K., 7 Mar 2019, In : Mathematics in Engineering. 1, 2, p. 281-308 28 p.

Research output: Contribution to journalArticle

Open Access

Stability of high-energy solitary waves in Fermi-Pasta-Ulam-Tsingou chains

Herrmann, M. & Matthies, K., 1 Sep 2019, In : Transactions of the American Mathematical Society. 372, 5, p. 3425–3486 62 p.

Research output: Contribution to journalArticle

Open Access
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34 Downloads (Pure)
2018

Derivation of a Nonautonomous Linear Boltzmann Equation from a Heterogeneous Rayleigh Gas

Matthies, K. & Stone, G., 1 Jul 2018, In : Discrete and Continuous Dynamical Systems - Series A. 38, 7, p. 3299-3355 57 p.

Research output: Contribution to journalArticle

Open Access
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20 Downloads (Pure)

The derivation of the linear Boltzmann equation from a Rayleigh gas particle model

Matthies, K., Stone, G. R. & Theil, F., 1 Feb 2018, In : Kinetic and Related Models. 11, 1, p. 137-177 41 p., 14450.

Research output: Contribution to journalArticle

Open Access
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2 Citations (Scopus)
120 Downloads (Pure)
2016

Low regularity justification results for envelope approximations of nonlinear wave packets in periodic media

Matthies, K. & Uecker, H., 10 Aug 2016, In : Asymptotic Analysis. 99, 1-2, p. 53-65

Research output: Contribution to journalArticle

Open Access
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126 Downloads (Pure)
2015

Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

Herrmann, M. & Matthies, K., Aug 2015, In : Nonlinearity. 28, 8, p. 2767-2789

Research output: Contribution to journalArticle

Open Access
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3 Citations (Scopus)
124 Downloads (Pure)
2014
Open Access
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1 Citation (Scopus)
128 Downloads (Pure)
2013

Can equations of equilibrium predict all physical equilibria? A case study from Field Dislocation Mechanics

Das, A., Acharya, A., Zimmer, J. & Matthies, K., Nov 2013, In : Mathematics and Mechanics of Solids. 18, 8, p. 803-822 20 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

Subsonic phase transition waves in bistable lattice models with small spinodal region

Herrmann, M., Matthies, K., Schwetlick, H. & Zimmer, J., 3 Sep 2013, In : SIAM Journal on Mathematical Analysis (SIMA). 45, 5, p. 2625-2645 21 p.

Research output: Contribution to journalArticle

Open Access
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6 Citations (Scopus)
137 Downloads (Pure)
2012

A semigroup approach to the justification of kinetic theory

Matthies, K. & Theil, F., 2012, In : SIAM Journal on Mathematical Analysis (SIMA). 44, 6, p. 4345–4379 35 p.

Research output: Contribution to journalArticle

Open Access
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4 Citations (Scopus)
124 Downloads (Pure)
2010

Travelling wave solutions for a quasilinear model of field dislocation mechanics

Acharya, A., Matthies, K. & Zimmer, J., Dec 2010, In : Journal of the Mechanics and Physics of Solids. 58, 12, p. 2043-2053 11 p.

Research output: Contribution to journalArticle

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11 Citations (Scopus)
122 Downloads (Pure)

Validity and failure of the Boltzmann approximation of kinetic annihilation

Matthies, K. & Theil, F., 1 Feb 2010, In : Journal of Nonlinear Science. 20, 1, p. 1-46 46 p.

Research output: Contribution to journalArticle

Open Access
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5 Citations (Scopus)
115 Downloads (Pure)
2009

Small planar travelling waves in two-dimensional networks of coupled oscillators

Pfrang, C. & Matthies, K., 2009, In : Dynamical Systems: An International Journal. 24, 2, p. 157-170 14 p.

Research output: Contribution to journalArticle

Open Access
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1 Citation (Scopus)
120 Downloads (Pure)
2008

Exponential averaging under rapid quasiperiodic forcing

Matthies, K., 2008, In : Advances in Differential Equations. 13, 5-6, p. 427-456 30 p.

Research output: Contribution to journalArticle

1 Citation (Scopus)
2007

Exponential averaging for traveling wave solutions in rapidly varying periodic media

Matthies, K., Schneider, G. & Uecker, H., 2007, In : Mathematische Nachrichten. 280, 4, p. 408-422 15 p.

Research output: Contribution to journalArticle

4 Citations (Scopus)

Exponential homogenization of linear second order elliptic PDEs with periodic coefficients

Kamotski, V., Matthies, K. & Smyshlyaev, V. P., 12 Jan 2007, In : SIAM Journal on Mathematical Analysis (SIMA). 38, 5, p. 1565-1587 23 p.

Research output: Contribution to journalArticle

Open Access
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8 Citations (Scopus)
115 Downloads (Pure)
2006

Wave pinning in strips

Matthies, K. & Wayne, C. E., Oct 2006, In : Proceedings of the Royal Society of Edinburgh Section A - Mathematics. 136, 5, p. 971-995 25 p.

Research output: Contribution to journalArticle

Open Access
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6 Citations (Scopus)
119 Downloads (Pure)
2005

Homogenisation of exponential order for elliptic systems in infinite cylinders

Matthies, K., 2005, In : Asymptotic Analysis. 43, 3, p. 205-232

Research output: Contribution to journalArticle

Open Access
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6 Citations (Scopus)
29 Downloads (Pure)
2003
Open Access
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3 Citations (Scopus)
91 Downloads (Pure)

Exponential averaging for Hamiltonian evolution equations

Matthies, K. & Scheel, A., 2003, In : Transactions of the American Mathematical Society. 355, 2, p. 747-773

Research output: Contribution to journalArticle

16 Citations (Scopus)
4 Citations (Scopus)
123 Downloads (Pure)

Geometric solitary waves in a 2D mass-spring lattice

Friesecke, G. & Matthies, K., Feb 2003, In : Discrete and Continuous Dynamical Systems - Series B. 3, 1, p. 105-144

Research output: Contribution to journalArticle

Open Access
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28 Citations (Scopus)
114 Downloads (Pure)
2002

Atomic-scale localization of high-energy solitary waves on lattices

Friesecke, G. & Matthies, K., Nov 2002, In : Physica D: Nonlinear Phenomena. 171, 4, p. 211-220 10 p.

Research output: Contribution to journalArticle

Open Access
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36 Citations (Scopus)
120 Downloads (Pure)
2001
File
26 Citations (Scopus)
134 Downloads (Pure)
1999

A Subshift of Finite Type in the Takens-Bogdanov Bifurcation with D 3 Symmetry

Matthies, K., 1999, In : Documenta Mathematica. 4, p. 463-485 23 p.

Research output: Contribution to journalArticle