Abstract
We are concerned with an attraction-repulsion Keller-Segel system with a degradation source of a subquadratic power in a bounded domain with smooth boundary in dimensions two and higher. There are three different cases depending on correlations of parameters of the system, which are attraction-dominating, repulsion-dominating, and attraction-repulsion balancing, respectively. We establish the existence of generalized solutions to the system with admissible powers of degradation corresponding to each case. It turns out that, as expected, the attraction-dominating case requires strictly larger powers of degradation than repulsion-dominating one. It is, however, noteworthy that our result presents the power of degradation for the attraction-repulsion balancing case to be the smallest compared to other cases.
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