Lower Estimate of the Attractor Dimension for a Chemotaxis Growth System

By M. Aida, Tohru Tsujikawa, Messoud A. Efendiev, A. Yagi, Masayasu Mimura. 2006

92 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/419f990f718d74d6db801e7fce2581120ee123c3

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In Biomedical Engineering

Citations in the corpus

Emergence of large population densities despite logistic growth restrictions in fully parabolic chemotaxis systems (2017, background): “In presence of small values of μ when no such proliferation-dominated behavior can be expected, only little seems known beyond results on existence and dimension of exponential attractors in two-dimensional frameworks ([17], [16], [2]); after all, large-time extinction phemonena, as numerically obse”
Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source (2014, background): “Further steps in this direction may hopefully lead to an even more detailled insight, much in the spirit of [13, 1], into the long-time behaviour of solutions to (1) in dimension 3 for small, positive μ.”
On the weakly competitive case in a two-species chemotaxis model (2016, result): “[37], emphasized by attractor results in [20, 32, 1, 33] or illustrated by recent results on transient growth phenomena in [51], [21].”
A Chemotaxis System with Logistic Source (2007, background): “Numerics and experiments show the existence of patterning solutions (Aida et al., 2006).”
Boundedness and global existence in the higher-dimensional parabolic–parabolic chemotaxis system with/without growth source (2015, unknown): “See more in [2,32,38].”
Spatio-temporal chaos in a chemotaxis model (2011, methodology): “[25] study a typical bifurcation route for increasing chemotactic sensitivity in 2D.”
Very weak global solutions to a parabolic–parabolic chemotaxis-system with logistic source (2016, methodology): “In the chemotaxis-system context, this is mathematically formulated by adding to the rst equation of system (1) a polynomial function depending on u and, possibly, on |∇u|; speci cally, in such models, the contribution of any monomial with positive (negative) coe cient corresponds to a birth (death)”