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

Shaohua Chen

doi:10.3934/cpaa.2006.5.919

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2006, Volume 5, Issue 4: 919-928. Doi: 10.3934/cpaa.2006.5.919

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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

Received: January 31, 2006

Revised: June 30, 2006

Published: November 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 35J55.

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