A Chemotaxis System with Logistic Source

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Boundedness in a two‐species chemotaxis system (2015, background): “In particular, the work in [17] addresses the case D 0 and asserts global existence of solutions under the sufficient condition > .”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, background): “1), all solutions emanating from reasonably regular initial data are global in time and remain bounded whenever n ≤ 2 and μ1 > 0 is arbitrary ([28]), or n ≥ 3 and μ1 is sufficiently large ([38]), with the corresponding condition on the size of μ1 being even explicit in the parabolic-elliptic counter”
Very weak global solutions to a parabolic–parabolic chemotaxis-system with logistic source (2016, background): “[22]) weak solutions exist for arbitrary μ > 0 and they are smooth and globally classical if μ > n−2 n .”
Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case (2012, background): “Notice that the regularity properties of solutions to Keller-Segel type equations with reaction terms have been studied earlier in [25, 28, 27], but in a different setting.”
Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion (2019, methodology): “Performing the similar (test function) argument as done in [21], we derive some regularity results for (4.”