Exponential attractor for a chemotaxis-growth system of equations

By Koichi Osaki, Tohru Tsujikawa, A. Yagi, Masayasu Mimura. 2002

407 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/063aa8fd87f85a731eac2b8c299018579f202c74

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Citations in the corpus

Spatio-temporal chaos in a chemotaxis model (2011, background): “[24] studied (3)–(4) on a two-dimensional bounded domain under homogeneous Neumann boundary conditions and the logistic form for f (u).”
A user’s guide to PDE models for chemotaxis (2009, background): “A general 1D case was studied in Osaki and Yagi [75] and applies to our models (M1), (M2a), and (M2b).”
Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction (2011, background): “1): In [19] it was shown that if f(u) = μu(1−u) with some μ > 0, then in planar bounded domains Ω ⊂ R(2), all solutions of the corresponding initialboundary value problem for”
A Chemotaxis System with Logistic Source (2007, methodology): “The ideas used to prove global existence of weak solutions in Osaki et al. (2002) may be used to study the case with nonlinear sensitivity function v satisfying sup s≥0 ∣∣∣∣d s ds ∣∣∣∣ < For the case when the rate d is large (where “d” is the diffusion coefficient of the chemical substance “v”) one…”
Boundedness of solutions to a quasilinear parabolic–elliptic Keller–Segel system with logistic source (2014, background): “The same conclusion is true for the parabolic–parabolic system with > 0 when either n D 2 [14, 15] or n 3 with > 0 for some 0 > 0 [16].”
Chemotaxis and growth system with singular sensitivity function (2005, unknown): “In the previous paper [13], we have studied the case where the sensitivity function is a smooth function of (cid:26) 2 [0 ; 1 ) without singularity at (cid:26) = 0 and has uniformly bounded derivatives up to the third order (see the condition ( (cid:31) ) of [13]).”