Simultaneous finite time blow-up in a two-species model for chemotaxis

By Elio Espejo, Angela Stevens, Juan J. López Velázquez. 2009

109 citations recorded by the source corpus.

Subfields: Cell Biology, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/594578f1068b113f3e86cac3f3c1f1f7f2524845

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In Cell Biology

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Citations in the corpus

Remarks on the blowup and global existence for a two species chemotactic Keller–Segel system in 2 (2011, background): “[6], Section 2 , it reduces to ∂tu1 = μ∆u1 − χ1∇ · (u1∇v), ∂tu2 = ∆u2 − χ2∇ · (u2∇v), ε∂tv(x, t) = ∆v + u1 + u2, where ε = μ D .”
A Note on non-simultaneous blow-up for a drift-diffusion model (2010, methodology): “Using regularity theory for parabolic equations as in [1], Lemma 6, we then obtain the bound u2 = 1r ∂M2 ∂r ≤ C, for a suitable constant C > 0.”
Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant (2015, background): “More recently, systems of two species with one chemoattractant have been studied by different research groups, the flnite-time blow-up in bounded domains for the ParabolicParabolic-Elliptic issue has been analyzed by Espejo, Stevens and Velázquez [7] and [8] for simultaneous and non-simultaneous blo”
On the weakly competitive case in a two-species chemotaxis model (2016, background): “…situation of several species is to consider two species (or two subpopulations of one species) that react to the same signalling substance they both produce, as occurring in the differentiation of cell-types during slime mold formation in populations of Dictyostelium discoideum, cf. e.g. [29, 44].”
Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics (2016, unknown): “Without kinetic terms, that is, when μ1 = μ2 = 0, the resulting system then inherits some important properties from the original Keller-Segel model for single-species chemotaxis; in particular, the striking phenomenon of finite-time blow-up, known to occur in both parabolic-elliptic and fully parabo”
Boundedness, blowup and critical mass phenomenon in competing chemotaxis (2016, unknown): “We also point out that the critical mass phenomenon for the three-component chemotaxis model with two species and one signal was studied in [8,20], which is apparently different from the ARKS model (1.”