Chemotaxis and growth system with singular sensitivity function

By M. Aida, Koichi Osaki, Tohru Tsujikawa, A. Yagi, Masayasu Mimura. 2005

71 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/c8317eba3a97d25db7e5d3327239f8e502cf53f3

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Citations in the corpus

Boundedness and global existence in the higher-dimensional parabolic–parabolic chemotaxis system with/without growth source (2015, methodology): “[37,1], for example), where the chemotactic sensitivities were assumed to have special structures.”
Global existence for chemotaxis with finite sampling radius (2006, background): “Several of these regularizations have been studied in the literature , including saturation effects (e.g. Othmer and Stevens [24], Rivero et al. [31], Aida et al. [1]), volume filling (e.g. Painter and Hillen [25]), attraction-repulsion mechanisms (e.g. Luca et al. [17] Renclawowicz and Hillen [30])”
A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity (2015, background): “In [13], the authors prove global existence and investigate the asymptotic behaviour of solutions to a system incorporating logistic growth terms in addition to general sensitivities with singularity at v D 0.”
Boundedness in the Higher-Dimensional Parabolic-Parabolic Chemotaxis System with Logistic Source (2010, background): “1) but also for a number of variants with more general cross-diffusion terms in the PDE for the cell density [1, 15, 16].”
Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems (2017, background): “and initially discussed in [1] from a rigorous perspective, have recently been shown to necessarily be of local nature in the sense that for each global solution, the associated total mass of cells always persists throughout evolution ([24]).”