Analysis of hysteretic reaction-diffusion systems

Quarterly of Applied Mathematics

Volumn 56, Issue 1, 1998, Pages 89-106

  Chiu, Chichia ^a   Walkington, Noel ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Accretion pattern formation; Reaction diffusion equations; Semi groups

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; GROWTH KINETICS; MATHEMATICAL MODELS;

REACTION DIFFUSION SYSTEMS;

BACTERIA;

EID: 0032028995     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1604805     Document Type: Article

References (19)

1. N. E. Britton, Reaction-Diffusion Equations and Their Applications to Biology, Academic Press, New York, 1986
2. E. O. Budriené, A. A. Polezhaev, and M. O. Ptitsyn, Mathematical modeling of intercellular regulation causing the formation of spatial structures in bacterial colonies, J. Theor. Biol. 135, 323-341 (1988)
3. J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1985
4. C. Chiu, F. C. Hoppensteadt, and W. Jäger, Analysis and computer simulation of accretion patterns in bacterial cultures, to appear
5. C. Chiu and N. J. Walkington, An ADI method for hysteretic reaction-diffusion systems, SIAM J. Numer. Anal. 34, 1185-1206 (1997)
6. F. C. Hoppensteadt and W. Jäger, Pattern formation by bacteria, Lecture Notes in Biomath. 38, 68-81 (1980)
7. F. C. Hoppensteadt, W. Jäger, and C. Pöppe, A hysteresis model for bacterial growth patterns, in Modelling of Patterns in Space and Time, W. Jäger and J. D. Murray, eds., Lecture Notes in Biomath. vol. 55, Springer-Verlag, Berlin, New York, 1984, pp. 123-134
8. G. Hauser, Uber Fäulnisslacterien und deren Beriehungen zur Septicämie, Leipzig: F. G. W. Vogel, 1885
9. U. Hornung and R. E. Showalter, Pde-models with hysteresis on the boundary, in A. Visintin, editor, Models of Hysteresis, volume 286, Research Notes in Mathematics, Pitman, 1983, pp. 30-38
10. U. Hornung and R. E. Showalter, Elliptic-parabolic equations with hysteresis boundary conditions, SIAM J. Mathematical Analysis 26, 775-790 (1995)
11. D. L. Lewis and D. K. Gattie, The ecology of quiescent microbes, ASM News 57, 27-32 (1991)
12. P. Gerhardt, et al., Manual of Methods for General Bacteriology, P. Gerhardt, editor-in-chief, Amer. Soc. for Microbiology, Washington, DC 20006, 1981
13. H. M. Lieberstein, Theory of Partial Differential Equations, Mathematics in Science and Engineering, vol. 93, Academic Press, New York and London, 1972
14. T. D. Little and R. E. Showalter, Semilinear parabolic equations with Preisach hysteresis, Differential and Integral Equations 7, 1021-1040 (1994)
15. J. W. T. Wimpenney, J. P. Coombs, R. W. Lovitt, and S. G. Whittaker, A gel-stabilized model ecosystem for investigating microbial growth in spatially ordered solute gradients, J. Gen. Microbio. 127, 277-287 (1981)
16. J. W. Macki, P. Nistri, and P. Zecca, Mathematical Models for Hysteresis, SIAM Review, Vol. 35, No. 1, 1993, pp. 94-123
17. J. Monod, Recherches sur La Croissance de Cultures Bacteriennes, Hermann et Cie, Paris, 1942
18. J. D. Murray, Mathematical Biology, Biomathematics Texts, Springer-Verlag, 1989
19. T. E. Shehata and A. G. Marr, Synchronous growth of enteric bacteria, J. Bacteriology 103, 789 (1970)