Boundedness in quasilinear Keller–Segel systems of parabolic–parabolic type on non-convex bounded domains
By Sachiko Ishida, Kiyotaka Seki, Tomomi Yokota. 2014
389 citations recorded by the source corpus.
Subfields: Cell Biology, Modeling and Simulation, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/9029de619fe1d596bfee00eb5dc398852a2f147f
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Citations in the corpus
- Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates (2015, background): “in [11] for a related framework, this additional requirement can be removed; in order not to further complicate our presentation, we refrain from addressing this more general setting here.”
- Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “The proofs are either contained in or adapted from the articles [26, 17, 44].”
- Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, methodology): “7 Bounds for nε and ∇cε in L(Ω) Now our knowledge on regularity of uε is sufficient to allow for the derivation of L p bounds for both nε and ∇cε by means of an analysis of a functional combining ∫ Ω n p ε with ∫ Ω |∇cε| with arbitrarily large p and suitably chosen q = q(p), thus following an approa”
- Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system (2017, background): “For instance, quite a comprehensive understanding could be achieved in the case when D = D(u) > 0 and χ = χ(u) ≥ 0 are suitably smooth, independent of the signal concentration v = v(x, t) and exclusively depending on the population density u = u(x, t): Then, namely, known results indicate that essen”
- Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, background): “Global existence, boundedness or blowup of solutions in more general quasilinear parabolic– parabolic chemotaxis systems with nonlinear sensitivity functions and source term have been studied extensively, see for example, [11,12,25,26,34,44,48,49,59,61,62].”
- Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities (2016, background): “By arguments relying on estimates from [25] or [37], it has become possible to remove this assumption (cf.”