A Reaction-Diffusion-Advection Equation with a Free Boundary and Sign-Changing Coefficient
A Reaction-Diffusion-Advection Equation with a Free Boundary and Sign-Changing Coefficient
复制标题
具有自由边界和变号系数的反应扩散平流方程
DOI：
10.1007/s10440-015-0035-0
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发表时间：
2016
影响因子：
1.6
通讯作者：
Liu Zuhan
中科院分区：
文献类型：
--
作者：
Zhou Ling;Zhang Shan;Liu Zuhan
本文研究了一类具有自由边界和变号系数的反应扩散对流方程。主要目的是了解平流项对解的长时间行为的影响。更准确地说，我们证明了一个传播-消失的二分法结果，即物种要么成功地传播到无限大，并在新的环境中生存，或者它未能建立，并在长期内灭绝。当扩展发生时，扩展锋的扩展速度受平流的影响。在这种情况下，我们得到最好的可能的上限和下限的扩展前的扩展速度。此外，当环境在无穷远处渐近齐次时，这两个边界重合。
In this paper we investigate a reaction-diffusion-advection equation with a free boundary and sign-changing coefficient. The main objective is to understand the influence of the advection term on the long time behavior of the solutions. More precisely, we prove a spreading-vanishing dichotomy result, namely the species either successfully spreads to infinity asand survives in the new environment, or it fails to establish and dies out in the long run. When spreading occurs, the spreading speed of the expanding front is affected by the advection. In this situation, we obtain best possible upper and lower bounds for the spreading speed of the expanding front. Furthermore, when the environment is asymptotically homogeneous at infinity, these two bounds coincide.