Abstract
This paper is concerned with the positive solutions of some nonlocal dispersal equations. Observe that “blow-up” phenomenon occurs due to spatial degeneracies and linear reactions. It is interesting to investigate the sharp effects between degeneracy and reaction. By employing a parameter in the initial problem, we analyze the asymptotic limiting profiles of positive solutions. Our study reveals how the existence of sharp profiles is determined by degeneracies and reactions. Moreover, we may obtain six different blow-up speeds for sharp patterns and the results state that the simple nonlocal dispersal equation can also exhibit quite complex patterns.
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