Abstract
In this paper, we study the positive solutions of the diffusive logistic equations. It is shown that the asymptotic profiles of the positive solutions display differences between nonlocal dispersal equation and semilinear elliptic equation. When the degeneracy domain becomes small, we find that the positive solution of semilinear elliptic equation admits a blow-up profile. However, when the non-degeneracy domain becomes large, the positive solution of nonlocal equation exhibits a blow-up profile.
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