Dynamical spike solutions in a nonlocal model of pattern formation
Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a rea...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
27 March 2018
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| In: |
Nonlinearity
Year: 2018, Volume: 31, Issue: 5 |
| ISSN: | 1361-6544 |
| DOI: | 10.1088/1361-6544/aaa5dc |
| Online Access: | Resolving-System, Volltext: http://dx.doi.org/10.1088/1361-6544/aaa5dc Verlag, Volltext: http://stacks.iop.org/0951-7715/31/i=5/a=1757 
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| Author Notes: | Anna Marciniak-Czochra, Steffen Härting, Grzegorz Karch and Kanako Suzuki |
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| 520 | |a Coupling a reaction-diffusion equation with ordinary differential equa- tions (ODE) may lead to diffusion-driven instability (DDI) which, in contrast to the classical reaction-diffusion models, causes destabilization of both, constant solutions and Turing patterns. Using a shadow-type limit of a reaction-diffusion-ODE model, we show that in such cases the instability driven by nonlocal terms (a counterpart of DDI) may lead to formation of unbounded spike patterns. | ||
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