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