Wavefronts for a nonlinear nonlocal bistable reaction–diffusion equation in population dynamics
Wavefronts for a nonlinear nonlocal bistable reaction–diffusion equation in population dynamics
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DOI：
10.1016/j.jde.2017.07.019
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发表时间：
2017-01
影响因子：
2.4
通讯作者：
Li Chen;E. Latos;Jing Li
中科院分区：
文献类型：
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作者：
Li Chen;E. Latos;Jing Li
本文研究了非线性非局部双稳态反应扩散方程 ∂ u∂ t=∂ 2 u∂ x 2+ u 2 (1− J σ⁎ u)− d u,(t, x)ε(0,∞)× R 的波前，其中 J σ (x)=(1/σ) J (x/σ) 和 ∫ R J (x) d x= 1。证明存在c⁎(σ)，使得对于所有c≥c⁎(σ)，单调波前(c, ω)可以由两个正平衡点连接。另一方面，存在 c⁎(σ)，使得模型允许半波前 (c⁎(σ), ω)，其中 ω (−∞)= 0。此外，结果表明，对于足够小的 σ，半波前实际上是将 0 连接到最大平衡的波前。此外，波前收敛于局部问题的波前，σ→0。
The wavefronts of a nonlinear nonlocal bistable reaction–diffusion equation,∂ u∂ t=∂ 2 u∂ x 2+ u 2 (1− J σ⁎ u)− d u,(t, x)∈(0,∞)× R, with J σ (x)=(1/σ) J (x/σ) and∫ R J (x) d x= 1 are investigated in this article. It is proven that there exists a c⁎(σ) such that for all c≥ c⁎(σ), a monotone wavefront (c, ω) can be connected by the two positive equilibrium points. On the other hand, there exists a c⁎(σ) such that the model admits a semi-wavefront (c⁎(σ), ω) with ω (−∞)= 0. Furthermore, it is shown that for sufficiently small σ, the semi-wavefronts are in fact wavefronts connecting 0 to the largest equilibrium. In addition, the wavefronts converge to those of the local problem as σ→ 0.