TY - JOUR

T1 - The diffusion limit of transport equations II

T2 - Chemotaxis equations

AU - Othmer, Hans G.

AU - Hillen, Thomas

PY - 2002/4

Y1 - 2002/4

N2 - In this paper, we use the diffusion-limit expansion of transport equations developed earlier [T. Hillen and H. G. Othmer, SIAM J. Appl. Math., 61 (2000), pp. 751-775] to study the limiting equation under a variety of external biases imposed on the motion. When applied to chemotaxis or chemokinesis, these biases produce modification of the turning rate, the movement speed, or the preferred direction of movement. Depending on the strength of the bias, it leads to anisotropic diffusion, to a drift term in the flux, or to both, in the parabolic limit. We show that the classical chemotaxis equation-which we call the Patlak-Keller-Segel-Alt (PKSA) equation-arises only when the bias is sufficiently small. Using this general framework, we derive phenomenological models for chemotaxis of flagellated bacteria, of slime molds, and of myxobacteria. We also show that certain results derived earlier for one-dimensional motion can easily be generalized to two- or three-dimensional motion as well.

AB - In this paper, we use the diffusion-limit expansion of transport equations developed earlier [T. Hillen and H. G. Othmer, SIAM J. Appl. Math., 61 (2000), pp. 751-775] to study the limiting equation under a variety of external biases imposed on the motion. When applied to chemotaxis or chemokinesis, these biases produce modification of the turning rate, the movement speed, or the preferred direction of movement. Depending on the strength of the bias, it leads to anisotropic diffusion, to a drift term in the flux, or to both, in the parabolic limit. We show that the classical chemotaxis equation-which we call the Patlak-Keller-Segel-Alt (PKSA) equation-arises only when the bias is sufficiently small. Using this general framework, we derive phenomenological models for chemotaxis of flagellated bacteria, of slime molds, and of myxobacteria. We also show that certain results derived earlier for one-dimensional motion can easily be generalized to two- or three-dimensional motion as well.

KW - Aggregation

KW - Chemotaxis equations

KW - Diffusion approximation

KW - Transport equations

KW - Velocity-jump processes

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U2 - 10.1137/S0036139900382772

DO - 10.1137/S0036139900382772

M3 - Article

AN - SCOPUS:0036553052

VL - 62

SP - 1222

EP - 1250

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 4

ER -