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December  2006, 5(4): 919-928. doi: 10.3934/cpaa.2006.5.919

Some properties for the solutions of a general activator-inhibitor model

Shaohua Chen 1,

1. 

Department of Mathematics, Physics & Geology, Cape Breton University, Sydney, NS, Canada, B1P 6L2, Canada

Received  February 2006 Revised  July 2006 Published  September 2006

This paper deals with the generalized Activator-Inhibitor model which originally arose in studies of pattern-formation in biology and has interesting and challenging mathematical properties. We study the long time existence of solutions as well as the boundedness and blowup properties for some special cases. We also obtain a priori estimates of stationary solutions followed by some numerical solutions with moving mesh methods.
Keywords: blowup solutions, stationary solutions., boundedness, Activator-Inhibitor model.
Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 35J5.
Citation: Shaohua Chen. Some properties for the solutions of a general activator-inhibitor model. Communications on Pure & Applied Analysis, 2006, 5 (4) : 919-928. doi: 10.3934/cpaa.2006.5.919
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