Prevention of blow-up by fast diffusion in chemotaxis

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Asymptotic dynamics of the one‐dimensional attraction–repulsion Keller–Segel model (2015, background): “1) such that the solution of the modified system is bounded for any magnitude of cell mass (see a review article [4] and recent development in [5, 6]).”
Boundedness, blowup and critical mass phenomenon in competing chemotaxis (2016, background): “see [4,5,15,16,19,29,31,32,37,40,41] and the references therein, and review articles [13,18,39]).”
Boundedness of the attraction–repulsion Keller–Segel system (2015, background): “This particular structure motivated a vast amount of mathematical studies in the past (see review articles [7,9,27]) and recent studies [3,8,26,28,29], where most of works were focused at whether the solution blows up or not (see some early works in [10,19,20] in this area).”