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Title: A dual-gradient chemotaxis system modeling the spontaneous aggregation of microglia in Alzheimer’s disease
Authors: Jin, HY
Wang, ZA 
Keywords: Attraction–repulsion
Higher dimensions
Pattern formation
Spontaneous aggregation
Issue Date: 2018
Publisher: World Scientific
Source: Analysis and applications, 2018, v. 16, no. 3, p. 307-338 How to cite?
Journal: Analysis and applications 
Abstract: In this paper, we consider the following dual-gradient chemotaxis model (Formula presented.) with (Formula presented.) for (Formula presented.) and (Formula presented.) for (Formula presented.), where (Formula presented.) is a bounded domain in (Formula presented.) with smooth boundary, (Formula presented.) and (Formula presented.). The model was proposed to interpret the spontaneous aggregation of microglia in Alzheimer’s disease due to the interaction of attractive and repulsive chemicals released by the microglia. It has been shown in the literature that, when (Formula presented.), the solution of the model with homogeneous Neumann boundary conditions either blows up or asymptotically decays to a constant in multi-dimensions depending on the sign of (Formula presented.), which means there is no pattern formation. In this paper, we shall show as (Formula presented.), the uniformly-in-time bounded global classical solutions exist in multi-dimensions and hence pattern formation can develop. This is significantly different from the results for the case (Formula presented.). We perform the numerical simulations to illustrate the various patterns generated by the model, verify our analytical results and predict some unsolved questions. Biological applications of our results are discussed and open problems are presented.
ISSN: 0219-5305
EISSN: 1793-6861
DOI: 10.1142/S0219530517500087
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