Mathematical analysis of a model describing the invasion of bacteria in burn wounds

Nonlinear Analysis, Theory, Methods and Applications

Volumn 66, Issue 5, 2007, Pages 1118-1140

  Hilhorst, D ^a   King, J R ^b   Roger M ^c  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^c EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Reaction diffusion systems; Singular limit; Stefan problems

Indexed keywords

BACTERIA; BOUNDARY VALUE PROBLEMS; PARAMETER ESTIMATION; PROBLEM SOLVING;

REACTION-DIFFUSION SYSTEMS; SINGULAR LIMIT; STEFAN PROBLEMS;

NONLINEAR EQUATIONS;

EID: 33845330570     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2006.01.009     Document Type: Article

References (16)

1. Anguige K., King J.R., and Ward J.P. Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured pseudomonas aeruginosa population. J. Math. Biol. 51 5 (2005) 557-594
2. Crooks E.C.M., Dancer E.N., Hilhorst D., Mimura M., and Ninomiya H. Spatial segregation limit of a competition-diffusion system with Dirichlet boundary conditions. Nonlinear Anal. Real World Appl. 5 4 (2004) 645-665
3. Dancer E.N., Hilhorst D., Mimura M., and Peletier L.A. Spatial segregation limit of a competition-diffusion system. European J. Appl. Math. 10 2 (1999) 97-115
4. Dunford N., and Schwartz J.T. Linear operators. Part I (1988), Wiley Classics Library. John Wiley & Sons Inc., New York
5. Eymard R., Hilhorst D., van der Hout R., and Peletier L.A. A reaction-diffusion system approximation of a one-phase stefan problem. In: Menaldi L., Rofman E., and Sulem A. (Eds). Optimal Control and Partial Differential Equations (2001)
6. Evans L.C. Partial differential equations. Graduate Studies in Mathematics vol. 19 (1998), American Mathematical Society
7. Hilhorst D., Iida M., Mimura M., and Ninomiya H. A competition-diffusion system approximation to the classical two-phase Stefan problem. Japan J. Indust. Appl. Math. 18 2 (2001) 161-180 Recent topics in mathematics moving toward science and engineering
8. D. Hilhorst, J.R. King, M. Röger, Travelling wave analysis of a model describing the invasion of bacteria in burn wounds (in preparation)
9. Hilhorst D., van der Hout R., and Peletier L.A. The fast reaction limit for a reaction-diffusion system. J. Math. Anal. Appl. 199 2 (1996) 349-373
10. Hilhorst D., van der Hout R., and Peletier L.A. Diffusion in the presence of fast reaction: the case of a general monotone reaction term. J. Math. Sci. Univ. Tokyo 4 3 (1997) 469-517
11. Hilhorst D., van der Hout R., and Peletier L.A. Nonlinear diffusion in the presence of fast reaction. Nonlinear Anal. 41 5-6 Ser. A: Theory Methods (2000) 803-823
12. King J.R., Koerber A.J., Croft J.M., Ward J.P., Sockett R.E., and Williams P. Modelling host tissue degradation by extracellular bacterial pathogens. Math. Med. Biol. 20 3 (2003) 227-260
13. Lieberman G.M. Second Order Parabolic Differential Equations (1996), World Scientific Publishing Co. Inc.
14. Ladyzhenskaya O.A., Solonnikov V.A., and Ural'tseva N.N. Linear and quasi-linear equations of parabolic type. Translations of Mathematical Monographs vol. 23 (1968), American Mathematical Society
15. Lunardi A. Analytic semigroups and optimal regularity in parabolic problems. Progress in Nonlinear Differential Equations and their Applications vol. 16 (1995), Birkhäuser Verlag
16. Ward J.P., King J.R., Koerber A.J., Croft J.M., Sockett R.E., and Williams P. Cell-signalling repression in bacterial quorum sensing. Math. Med. Biol. 21 (2004) 169-204