Nonlinear Instability for a Volume-Filling Chemotaxis Model with Logistic Growth
This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d-dimensional box Td=(0,π)d (d=1,2,3). It is proved that given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics al...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/248657 |
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| Summary: | This paper deals with a Neumann boundary value problem for a volume-filling chemotaxis model with logistic growth in a d-dimensional box Td=(0,π)d (d=1,2,3). It is proved that given any general perturbation of magnitude δ, its nonlinear evolution is dominated by the corresponding linear dynamics along a finite number of fixed fastest growing modes, over a time period of the order ln(1/δ). Each initial perturbation certainly can behave drastically different from another, which gives rise to the richness of patterns. |
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| ISSN: | 1085-3375 1687-0409 |