Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case

By Alexander V. Kiselev, Lenya Ryzhik. 2012

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Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. In continuation of our work [A. Kiselev and L. Ryzhik, “Biomixing by chemotaxis and enhancement of biological reactions,” Comm. Partial Differential Equations 37, 298–318 (2012)]10.1080/03605302.2011.589879, we consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by the studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We consider the case of the weakly coupled quadratic reaction term, which is the most natural from the biological point of view and was left open in Kiselev and Ryzh...

Subfields: Condensed Matter Physics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/1c8e8ceb2fcb4cc53ccdf75b2bf9fe6f8a650e29

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Citations in the corpus

Suppression of Chemotactic Explosion by Mixing (2015, background): “[31] or [22] for a simple proof), we have ‖ρ− ρ̄‖(3)L3 6 C‖ρ− ρ̄‖ 3− d 2 L2 ‖ρ‖ d 2 Ḣ1 6 ‖ρ‖(2) Ḣ1 + C1‖ρ− ρ̄‖ 12−2d 4−d L2 ,”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, background): “1) thereby covers the result of the recent modeling approaches for biomixing in [9], [18] and [19], but beyond this (1.”
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, background): “This may become substantially different in situations when different types of boundary conditions are considered, possibly accounting for signal influx, or when signal absorption is replaced with mechanisms of signal production by cells, as recently proposed and studied in contexts involving fluid i”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “As recent analytical findings show, already cell transport through a given fluid may substantially influence the solution behavior in certain Keller-Segel-type chemotaxis systems ([28], [29]); in fact, even complete suppression of blow-up may occur ([30]).”
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system (2015, methodology): “1) thereby includes the outcomes of the modeling approaches for biomixing recently presented by Espejo and Suzuki ([5]) on the basis of an original work by Kiselev and Ryzhik ([13], [14]).”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, unknown): “Related mechanisms of chemotaxis-fluid interaction also arise in different biological contexts such as biomixing-based fertilization strategies of certain benthic invertebrates [14,15].”