Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774222 | Journal of Differential Equations | 2017 | 38 Pages |
Abstract
In this paper, we study the nonlocal dispersal equation{ut=â«RNJ(xây)u(y,t)dyâu+λuâa(x,t)up in Ω¯Ã(0,+â),u(x,t)=0 in (RNâΩ¯)Ã(0,+â),u(x,0)=u0(x) in Ω¯, where ΩâRN is a bounded domain, λ and p>1 are constants. The dispersal kernel J is nonnegative. The function aâC(Ω¯ÃR) is nonnegative and T-periodic in t, but a(x,t) has temporal or spatial degeneracies (a(x,t) vanishes). We first study the periodic nonlocal eigenvalue problems with parameter and establish the asymptotic behavior of principal eigenvalues when the parameter is large. We find that the spatial degeneracy of a(x,t) always guarantees a principal eigenfunction. Then we consider the dynamical behavior of the equation if a(x,t) has temporal or spatial degeneracies. Our results indicate that only the temporal degeneracy can not cause a change of the dynamical behavior, but the spatial degeneracy always causes fundamental changes, whether or not the temporal degeneracy appears.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jian-Wen Sun, Wan-Tong Li, Zhi-Cheng Wang,