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A gradually slowing travelling band of chemotactic bacteria. (English) Zbl 0528.92004

MSC:
92Cxx Physiological, cellular and medical topics
92F05 Other natural sciences (mathematical treatment)
35Q99 Partial differential equations of mathematical physics and other areas of application
92C05 Biophysics
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[1] Adler, J.: Chemotaxis in bacteria. Ann. Rev. Biochem. 44, 341-356 (1975)
[2] Holz, M., Chen, S.-H.: Quasi-elastic light scattering from migrating chemotactic bands of Escherichia Coli. Biophys. J. 23, 15-31 (1978)
[3] Holz, M., Chen, S.-H.: Spatio-temporal structure of migrating chemotactic bands of E. coli travelling band profile. Biophys. J. 26, 243-261 (1979)
[4] Keller, E. F., Segel, L. A.: Travelling bands of chemotactic bacteria: a theoretical analysis. J. Theoret. Biol. 30, 235-248 (1971) · Zbl 1170.92308
[5] Odell, G. M.: Travelling bands of chemotactic microorganisms, p. 345 in Chapter 6 of: Mathematical models in molecular and cellular biology, L. A. Segel, ed., Cambridge: Cambridge Univ. Press 1980
[6] Keller, E. F., Odell, G. M.: Necessary and sufficient conditions for chemotactic bands. Math. Biosci. 27, 309-317 (1975) · Zbl 0346.92009
[7] Scribner, T. L., Segel, L. A., Rogers, E. H.: A numerical study of the formation and propagation of travelling bands of chemotactic bacteria. J. Theoret. Biol. 46, 189-219 (1974)
[8] Lapidus, J. R., Schiller, R.: A model of travelling bands of chemotactic bacteria. Biophys. J. 22, 1-13 (1978)
[9] Johnson, R. S.: On a asymptotic solution of the Korteweg-de-Vries equation with slowly varying coefficients. J. Fluid. Mech. 60, 813-824 (1973) · Zbl 0273.76012
[10] Alt, W.: Biased random walk models for chemotaxis and related diffusion approximation. J. Math. Biol. 9, 147-177 (1980) · Zbl 0434.92001
[11] Rosen, G.: On the propagation theory for bands of chemotactic bacteria. Math. Biosci. 20, 185-189 (1974) · Zbl 0281.92006
[12] Keller, E. F.: Assessing the Keller-Segel model: How has it fared? In: Biological Growth and Spread, Jäger, Rost, and Tauth, ed., Berlin-Heidelberg-New York: Springer 1980 · Zbl 0437.92003
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