In this paper, global-in-time existence and blow-up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria and the non-existence of nonconstant solutions are studied in certain cases.

中文翻译：

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一类带聚合反应扩散方程

在本文中，显示了聚集现象（包括趋化性）理论中出现的反应扩散方程的全局及时存在和爆炸结果。还介绍了相应的稳态问题的性质。此外，在某些情况下研究了围绕恒定平衡的稳定性和非恒定解的不存在。