The diffusion limit of transport equations II: Chemotaxis equations

SIAM Journal on Applied Mathematics

Volumn 62, Issue 4, 2002, Pages 1222-1250

  Othmer, Hans G ^a   Hillen, Thomas ^a  

^a University of Minnesota   (United States)

Author keywords

Aggregation; Chemotaxis equations; Diffusion approximation; Transport equations; Velocity jump processes

Indexed keywords

APPROXIMATION THEORY; CHEMICAL ANALYSIS; DIFFUSION; MATHEMATICAL MODELS; ONE DIMENSIONAL; THREE DIMENSIONAL; TWO DIMENSIONAL;

CHEMOKINESIS; CHEMOTAXIS EQUATIONS; DIFFUSION APPROXIMATION; DIFFUSION LIMIT; PATLAK-KELLER-SEGEL-ALT EQUATION; PHENOMENOLOGICAL MODELS; TRANSPORT EQUATIONS; VELOCITY JUMP PROCESS;

EQUATIONS OF MOTION;

EID: 0036553052     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139900382772     Document Type: Article

References (54)

1. Biased random walk models for chemotaxis and related diffusion approximations
2. Singular perturbation of differential integral equations describing biased random walks
3. How bacteria swim
4. Chemotaxis in escherichia coli analysed by three-dimensional tracking
5. Physics of chemoreception
6. Local and global solvability of some parabolic systems modelling chemotaxis
7. Adaptation kinetics in bacterial chemotaxis
8. Numerical solution of transport equations for bacterial chemotaxis: Effects of discretization of directional motion
9. Perturbation expansion of Alt's cell balance equations reduces to Segel's one-dimensional equations for shallow chemoattractant gradients
10. A continuum analysis of the chemotactic signal seen by Dictyostelium discoideum
11. A generalized transport model for biased cell migration in an anisotropic environment
12. Transport equations and indices for random and biased cell migration based on single cell properties
13. Quantitative analysis of cell motility and chemotaxis in Dictyostelium discoideum by using an image processing system and a novel chemotaxis chamber providing stationary chemical gradients
14. Measurement of bacterial random motility and chemotaxis coefficients II: Application of single-cell-based mathematical model
15. Measurement of bacterial random motility and chemotaxis coefficients I: Stopped-flow diffusion chamber assay
16. Global behavior of a reaction-diffusion system modelling chemotaxis
17. On diffusion by discontinuous movements and the telegraph equation
18. Singularity patterns in a chemotaxis model
19. The diffusion limit of transport equations derived from velocity-jump processes
20. Global existence for a parabolic chemotaxis model with prevention of overcrowding
21. Existence of weak solutions for a hyperbolic model for chemosensitive movement
22. Hyperbolic models for chemotaxis in 1-D
23. On explosions of solutions to a system of partial differential equations modelling chemotaxis
24. A stochastic model related to the telegrapher's equation
25. Mathematical aspects of bacterial chemotaxis
26. Initiation of slime mold aggregation viewed as an instability
27. Model for chemotaxis
28. Sensing the environment: Bacterial chemotaxis
29. Chapman-Enskog-Hilbert expansions for a class of solutions of the telegraph equation
30. Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
31. Mathematical theories of topotaxis
32. Models of dispersal in biological systems
33. Oscillatory cAMP signaling in the development of Dictyostelium discoideum
34. Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks
35. Development and applications of a model for cellular response to multiple chemotactic cues
36. A cell's sense of direction
37. Differentiation, cell sorting and proportion regulation in the slug stage of Dictyostelium discoideum
38. Random walk with persistence and external bias
39. Transport models for chemotactic cell populations based on individual cell behavior
40. Control of direction of flagellar rotation in bacterial chemotaxis
41. Theory of continuum random walks and applications to chemotaxis
42. A theoretical study of receptor mechanisms in bacterial chemotaxis
43. Mathematical models for cellular behavior
44. Chemical control of eukaryotic cell movement: A new model
45. A model of excitation and adaptation in bacterial chemotaxis
46. Some stochastic processes which arise from a model of the motion of a bacterium
47. Excitation, oscillations and wave propagation in G-protein-based model of signal transduction in Dictyostelium discoideum
48. Frequency and orientation of pseudopod formation of Dictyostelium discoideum amebae chemotaxing in a spatial gradient: Further evidence for a temporal mechanism
49. Reversible receptor methylation is essential for normal chemotaxis of Escherichia coli in gradients of aspartic acid