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Spreading under shifting climate by a free boundary model: Invasion of deteriorated environment
Communications in Contemporary Mathematics ( IF 1.2 ) Pub Date : 2020-12-03 , DOI: 10.1142/s0219199720500777 Yuanyang Hu 1, 2 , Xinan Hao 3 , Yihong Du 4
Communications in Contemporary Mathematics ( IF 1.2 ) Pub Date : 2020-12-03 , DOI: 10.1142/s0219199720500777 Yuanyang Hu 1, 2 , Xinan Hao 3 , Yihong Du 4
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In this paper, we consider a free boundary model in one space dimension which describes the spreading of a species subject to climate change, where favorable environment is shifting away with a constant speed c > 0 and replaced by a deteriorated yet still favorable environment. We obtain two threshold speeds c 1 < c 0 and a complete classification of the long-time dynamics of the model, which reveals significant differences between the cases 0 < c < c 1 , c = c 1 , c 1 < c < c 0 and c ≥ c 0 . For example, when c 1 < c < c 0 , for a suitably parameterized family of initial functions u 0 σ increasing continuously in σ , we show that there exists 0 < σ ∗ < σ ∗ < ∞ such that the species vanishes eventually when σ ∈ ( 0 , σ ∗ ] , it spreads with asymptotic speed c 1 when σ ∈ ( σ ∗ , σ ∗ ) , it spreads with forced speed c when σ = σ ∗ , and it spreads with speed c 0 when σ > σ ∗ . Moreover, in the last case, while the spreading front propagates with asymptotic speed c 0 , the profile of the population density function u ( t , x ) approaches a propagating pair consisting of a traveling wave with speed c and a semi-wave with speed c 0 .
中文翻译:
通过自由边界模型在变化的气候下传播:恶化环境的入侵
在本文中,我们考虑了一个空间维度上的自由边界模型,该模型描述了受气候变化影响的物种的扩散,其中有利的环境以恒定的速度远离C > 0 取而代之的是一个恶化但仍然有利的环境。我们获得两个阈值速度C 1 < C 0 以及模型长期动态的完整分类,揭示案例之间的显着差异0 < C < C 1 ,C = C 1 ,C 1 < C < C 0 和C ≥ C 0 . 例如,当C 1 < C < C 0 , 对于适当参数化的初始函数族你 0 σ 在不断增加σ , 我们证明存在0 < σ * < σ * < ∞ 这样物种最终会消失,当σ ∈ ( 0 , σ * ] , 它以渐近速度传播C 1 什么时候σ ∈ ( σ * , σ * ) , 它以强制速度传播C 什么时候σ = σ * ,并且传播速度很快C 0 什么时候σ > σ * . 此外,在最后一种情况下,扩展前沿以渐近速度传播C 0 , 人口密度函数的轮廓你 ( 吨 , X ) 接近由具有速度的行波组成的传播对C 和一个有速度的半波C 0 .
更新日期:2020-12-03
中文翻译:
通过自由边界模型在变化的气候下传播:恶化环境的入侵
在本文中,我们考虑了一个空间维度上的自由边界模型,该模型描述了受气候变化影响的物种的扩散,其中有利的环境以恒定的速度远离