RD‐systems with chemotaxis: Global existence, boundedness, and blow‐up of solutions

We study the finite time blow‐up of solutions to general RD‐systems with chemotaxis for multi‐species. Our result shows that the blow‐up is equivalent to the blow‐up of the Lr‐norms of the solutions for r exceeding some critical value rc. Under very loose conditions, we give the estimation of rc, re...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2022-03, Vol.45 (5), p.2516-2529
Main Authors: Xu, Xue, Huang, Sen‐Zhong
Format: Article
Language:English
Subjects:
blow‐up
global existence and boundedness
Norms
predator–prey
reaction–diffusion–taxis
Statistical methods
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Summary:We study the finite time blow‐up of solutions to general RD‐systems with chemotaxis for multi‐species. Our result shows that the blow‐up is equivalent to the blow‐up of the Lr‐norms of the solutions for r exceeding some critical value rc. Under very loose conditions, we give the estimation of rc, relying on a variant of Gagliardo–Nirenberg inequality, and a kind of bootstrap method which is very similar to the Alikakos–Moser iteration procedure.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7937