Global existence and infinite time blow-up of classical solutions to chemotaxis systems of local sensing in higher dimensions

By Kentarou Fujie, T. Senba. Nonlinear Analysis, 2021

57 citations recorded by the source corpus.

This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller–Segel system, we prove the absence of finite-time blow-up phenomenon in this system even in the supercritical case. It means that for any regular initial data, independently of the magnitude of mass, the classical solution exists globally in time in the higher dimensional setting. Moreover, for the exponential decaying motility case, it is established that solutions may blow up at infinite time for any magnitude of mass. In order to prove our theorem, we deal with some auxiliary identity as an evolution equation with a time dependent operator. In view of this new perspective, the direct consequence of the abstract theory is rich enough to establish global existence of the system.

Subfields: Modeling and Simulation, Molecular Biology, Oncology

View Paper: https://www.semanticscholar.org/paper/3c34569d72334e58b0115300972f1f6c1d0f34bc

Citations in the corpus

• A quantitative strong parabolic maximum principle and application to a taxis-type migration–consumption model involving signal-dependent degenerate diffusion (2022, unknown): “Besides basic results on global solvability (see [1], [14], [11], [10], [4], [15], [35], [34] and also [40]), several studies also include findings on asymptotic behavior, mainly identifying diffusion-dominated constellations in which solutions to either (1.”