Classical solutions and steady states of an attraction-repulsion chemotaxis in one dimension

Journal of Biological Dynamics

Volumn 6, Issue SUPPL. 1, 2012, Pages 31-41

  Liu, Jia ^a   Wang, Zhi An ^b  

^a UNIVERSITY OF WEST FLORIDA   (United States)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

attraction repulsion; chemotaxis; classical solutions; steady states

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CHEMOTAXIS; CYTOLOGY; DICTYOSTELIUM;

ANIMALS; CHEMOTAXIS; DICTYOSTELIUM; MODELS, BIOLOGICAL;

EID: 84860833132     PISSN: 17513758     EISSN: 17513766     Source Type: Journal    
DOI: 10.1080/17513758.2011.571722     Document Type: Article

References (15)

1. H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problemsFunction Spaces, Differential Operators and Nonlinear Analysis, Teubner Texte zur Mathematik, H.J. Schmeisser and H. Triebel, eds., Vol. 133, 1993,pp. 9-126
2. Brezis, H. 1998. Partial differential equations in the 20th century. Adv. Math, 135: 76-144.
3. Chuai, M., Zeng, W., Yang, X., Boychenko, V., Glazier, J. A. and Weijer, C. J. 2006. Cell movement during chick primitive streak formation. Dev. Biol, 296: 137-149.
4. Eisenbach, M. 2004. Chemotaxis, London: Imperial College Press.
5. Gates, M. A., Coupe, V. M., Torres, E. M., Fricker-Gates, R. A. and Dunnett, S. B. 2004. Spatially and temporally restricted chemoattractant and repulsive cues direct the formation of the nigro-sriatal circuit. Eur. J. Neurosci, 19: 831-844.
6. Horstmann, D. 2003. From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I. Jahresber. Deutsch. Math.-Verein, 105(3): 103-165.
7. Keller, E. F. and Segel, L. A. 1970. Initiation of slime mold aggregation viewed as in instability. J. Theor. Biol, 26: 399-415.
8. Li, C. 2004. The existence of solutions of elliptic equations with Neumann boundary conditions for superlinear problems. Acta. Math. Sin, 20: 965-976.
9. Luca, M., Chavez-Ross, A., Edelstein-Keshet, L. and Mogilner, A. 2003. Chemotactic signalling, microglia, and Alzheimer's disease senile plagues: is there a connection?. Bull Math. Biol, 65: 693-730.
10. Nirenberg, L. 1966. An extended interpolation inequality. Ann. Sc. Norm. Super. Pisa, 20: 733-737.
11. Painter, K. J. and Hillen, T. 2002. Volume-filling and quorum-sensing in models for chemosensitive movement. Can. Appl. Math. Q, 10(4): 501-543.
12. Schaaf, R. 1985. Stationary solutions of chemotaxis systems. Trans. Am. Math. Soc, 292: 531-556.
13. Suzuji, T. 2005. Free Energy and Self-interacting Particles, Boston, MA: Birkhäuser.
14. Wang, Z. A. and Hillen, T. 2007. Classical solutions and pattern formation for a volume filling chemotaxis model. Chaos, 17: 13 037108
15. Zhu, C. J. and Wang, Z. A. 2004. Decay rates of solutions to dissipative nonlinear evolution equations with ellipticity. Z. Angew. Math. Phys, 55: 994-1014.