Mathematical analysis and stability of a chemotaxis model with logistic term

Mathematical Methods in the Applied Sciences

Volumn 27, Issue 16, 2004, Pages 1865-1880

  Tello, J Ignacio ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Chemotaxis; Parabolic equations; Reinforced random walks; Stability of stationary solutions

Indexed keywords

BOUNDARY CONDITIONS; INTEGRATION; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

CHEMOTAXIS; PARABOLIC EQUATIONS; REINFORCED RANDOM WALKS; STABILITY OF STATIONARY SOLUTIONS;

MATHEMATICAL MODELS;

EID: 6444228071     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.528     Document Type: Article

References (12)

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, Velázquez JJL. A blow-up mechanism for a chemotaxis model. Ann. Scuola. Norm. Sup. Pisa. Cl. Sci. 1997; 24(4):633-683.
7. Jäger W, Luckhaus S. On explosions of solutions to a system of partial differential 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 diffusion 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.