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This paper deals with the generalized Activator-Inhibitor modelwhich originally arose in studies of pattern-formation in biologyand has interesting and challenging mathematical properties.We study the long time existence of solutions as well as theboundedness and blowup properties for some special cases. We alsoobtain a priori estimates of stationary solutions followed bysome numerical solutions with moving mesh methods.
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Shaohua Chen (2006) studied this question.
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