Abstract
In this paper, we consider the positive solutions of the nonlocal dispersal equation
where \(\Omega \subset \mathbb {R}^N\) is a bounded domain, \(\lambda ,\varepsilon \) and \(p>1\) are positive constants. The dispersal kernel J and the coefficient c(x) are nonnegative, but c(x) has a degeneracy in some subdomain of \(\Omega \). In order to study the influence of heterogeneous environment on the nonlocal system, we study the sharp spatial patterns of positive solutions as \(\varepsilon \rightarrow 0\). We obtain that the positive solutions always have blow-up asymptotic profiles in \(\bar{\Omega }\). Meanwhile, we find that the profiles in degeneracy domain are different from the domain without degeneracy.
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Sun, JW. Positive solutions for nonlocal dispersal equation with spatial degeneracy. Z. Angew. Math. Phys. 69, 11 (2018). https://doi.org/10.1007/s00033-017-0903-8
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DOI: https://doi.org/10.1007/s00033-017-0903-8