Summary:
The goal of the project is to develop and analyse numerical methods for computing moving patterns in time dependent partial differential equations. Examples are traveling waves in one, spiral waves in two, and scroll waves in three space dimensions. These occur in reaction diffusion systems and (non) viscous conservation laws that are equivariant with respect to the action of a Lie group. Our focus is the {\it freezing method\/} that allows to compute adaptive coordinate frames in which patterns become stationary. We investigate nonlinear stability of patterns, its relation to spectral properties, the influence of random perturbations, and we extend the method to handle multiple patterns.
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17023
Wolf-Jürgen Beyn, Etienne Emmrich, Janosch Rieger PDF
Semilinear Parabolic Differential Inclusions with One-sided Lipschitz Nonlinearities Project: B3 Published: J. Evol. Equ. 18, no. 3 (2018), 1319-1339 |
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17011
Alina Girod, Thorsten Hüls PDF
Project: B3
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On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation |
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16043
Wolf-Jürgen Beyn, Denny Otten PDF
Fredholm Properties and $L^p$-Spectra of Localized Rotating Waves in Parabolic Systems Project: B3 |
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16039
Wolf-Jürgen Beyn, Denny Otten, Jens Rottmann-Matthes PDF
Freezing Traveling and Rotating Waves in Second Order Evolution Equations Project: B3 Published: Patterns of dynamics, Springer Proc. Math. Stat. 205 (2017), 215–241 |
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16037
Thorsten Hüls PDF
Computing stable hierarchies of fiber bundles Project: B3 To appear: Discrete and Continuous Dynamical Systems - Series B (2016) |
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16022
Wolf-Jürgen Beyn, Denny Otten, Jens Rottmann-Matthes PDF
Computation and Stability of Traveling Waves in Second Order Evolution Equations Project: B3 Published: SIAM J. Numer. Anal. 56, no. 3 (2018), 1786-1817 |
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16007
Wolf-Jürgen Beyn, Denny Otten PDF
Spatial Decay of Rotating Waves in Reaction Diffusion Systems Project: B3 To appear: Dynamics of Partial Differential Equations (2016) Notes: 10.4310/DPDE.2016.v13.n3.a2 |
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15052
Thorsten Hüls PDF
Project: B3 Published: International Journal of Bifurcation and Chaos 26, no. 7 (2016), 1650118 pp. 10 Notes: http://dx.doi.org/10.1142/S0218127416501182
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On the approximation of stable and unstable fiber bundles of (non)autonomous ODEs – a contour algorithm |
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15042
Denny Otten PDF
A new $L^p$-Antieigenvalue Condition for Ornstein-Uhlenbeck Operators Project: B3 To appear: Journal of Mathematical Analysis and Applications (2016) |
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15030
Wolf-Jürgen Beyn, Thorsten Hüls, Andre Schenke PDF
Symbolic Coding for Noninvertible Systems: Uniform Approximation and Numerical Computation Project: B3 Published: Nonlinearity 29, no. 11 (2016), 3346-3384 Notes: doi:10.1088/0951-7715/29/11/3346 |
