eprintid: 45811
rev_number: 16
eprint_status: archive
userid: 1903
dir: disk0/00/04/58/11
datestamp: 2017-05-25 15:58:40
lastmod: 2021-05-21 09:48:47
status_changed: 2021-05-21 09:48:47
type: article
metadata_visibility: show
creators_name: Tello del Castillo, José Ignacio
creators_id: jtello@etsisi.upm.es
title: Mathematical analysis and stability of a chemotaxis model with logistic term.
publisher: John Wiley & Sons
rights: by-nc-nd
ispublished: pub
subjects: matematicas
full_text_status: public
keywords: Chemotaxis; stability of stationary solutions; parabolic equations; reinforced random walks
abstract: In this paper we study a non-linear system of dierential equations arising in chemotaxis. The system consists of a PDE that describes the evolution of a population and an ODE which models the concentration of a chemical substance. We study the number of steady states under suitable assumptions, the
existence of one global solution to the evolution problem in terms of weak solutions and the stability of the steady states.
date_type: published
date: 2004-06-17
publication: Mathematical methods in the applied sciences
volume: 27
number: 16
pagerange: 1865-1880
id_number: 10.1002/mma.528
institution: E_Informatica
department: Matematica_Aplicada
refereed: TRUE
issn: 0170-4214
official_url: http://onlinelibrary.wiley.com/doi/10.1002/mma.528/full
referencetext: REFERENCES

1. Keller EF, Segel LA. Initiation of slime mold aggregation viewed as an instability. Journal of Theoretical Biology 1970; 26:399 – 415.

2. Keller EF, Segel LA. A model for chemotaxis. Journal of Theoretical Biology 1971; 30:225 –234.

3. Corrias L, Perthame B, Zaag H. A chemotaxis model motivated by angiogenesis. Royal Mathematica Academiae
Scientasium Paris 2003; 336:141–146.

4. Fontelos MA, Friedman A, Hu B. Mathematical analysis of a model for the initiation of angiogenesis. SIAM
Journal on Mathematical Analysis 2002; 33:1330 –1355.

5. Friedman A, Tello JI. Stability of solutions of chemotaxis equations in reinforced random walks. Journal of
Mathematical Analysis and Applications 2002; 272:138 –163.

6. Herrero MA, Vel�azquez JJL. A blow-up mechanism for a chemotaxis model. Ann. Scuola. Norm. Sup. Pisa.
Cl. Sci. 1997; 24(4):633– 683.

7. J�ager W, Luckhaus S. On explosions of solutions to a system of partial dierential equations modeling
chemotaxis. Transactions of the American Mathematical Society 1992; 329:819 – 824.

8. Othmer HG, Stevens A. Aggregation, blowup, and collapse: the ABC’s of taxis in reinforced random walks.
SIAM Journal on Applied Mathematics 1997 57:1044 –1081.

9. Levine HA, Sleeman BP. A system of reaction diusion equations arising in the theory of reinforced random
walks. SIAM Journal on Applied Mathematics 1997; 57:683–730.

10. Anderson ARA, Chaplain MAJ. Continuous and discrete mathematical models of tumor-induced angiogenesis.
Bulletin of Mathematical Biology 1998; 60:857– 899.

11. Levine HA, Sleeman BP, Nilsen-Hamilton N. A mathematical modeling for the roles of pericytes and macrophages in the initiation of angiogenesis I. The role of protease inhibitors in preventing angiogenesis.
Mathematical Biosciences 2000; 168:75 –115.

12. Myerscough MR, Maini PK, Painter J. Pattern formation in a generalized chemotactic model. Bulletin of
Mathematical Biology 1998; 60:1–26.
comprojects_type: MINECO
comprojects_code: REN 2000/0766
comprojects_code: HPRN-CT-2002-00274
comprojects_leader: DGES
comprojects_leader: European Union
citation:   Tello del Castillo, José Ignacio  (2004).  Mathematical analysis and stability of a chemotaxis model with logistic term..   "Mathematical methods in the applied sciences", v. 27  (n. 16);   pp. 1865-1880.  ISSN 0170-4214.   https://doi.org/10.1002/mma.528 <https://doi.org/10.1002/mma.528>. 
document_url: http://oa.upm.es/45811/1/INVE_MEM_2004_250736.pdf