# American Institute of Mathematical Sciences

March  2012, 11(2): 735-746. doi: 10.3934/cpaa.2012.11.735

## The moving boundary problem in a chemotaxis model

 1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received  November 2010 Revised  July 2011 Published  October 2011

In this paper, we prove the local existence and uniqueness of a moving boundary problem modeling chemotactic phenomena. We also get the explicit representative for the moving boundary and show the finite-time blow-up and chemotactic collapse for the solution of the problem.
Citation: Hua Chen, Shaohua Wu. The moving boundary problem in a chemotaxis model. Communications on Pure & Applied Analysis, 2012, 11 (2) : 735-746. doi: 10.3934/cpaa.2012.11.735
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##### References:
 [1] E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability,, J. Theor. Biol., 26 (1970), 399.   Google Scholar [2] Miguel A. Herrero and Juan J. L. Velázquez, Singularity patterns in a chemotaxis model,, Math. Ann., 306 (1996), 583.   Google Scholar [3] W. Jäger and S. Luckhaus, On explosions of solutions to a system of partial differential equations modeling chemotaxis,, Trans. Amer. Math. Soc., 329 (1992), 819.   Google Scholar [4] V. Nanjundiah, Chemotaxis signal relaying and aggregation morphology,, J. Theor. Biol., 42 (1973), 63.   Google Scholar [5] T. Nagai, Blow-up of radially symmetric solutions to a chemotaxis system,, Adv. Math. Sci. Appl., 5 (1995), 581.   Google Scholar [6] S. Childress, Chemotactic collapse in two dimension,, Lecture Notes in Biomath., 55 (1984), 61.   Google Scholar
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