Propagation of KPP equations with advection in one-dimensional almost periodic media and its symmetry
Propagation of KPP equations with advection in one-dimensional almost periodic media and its symmetry
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DOI：
10.1016/j.aim.2022.108568
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发表时间：
2022-10
影响因子：
1.7
通讯作者：
Xing Liang;Tao Zhou
中科院分区：
文献类型：
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作者：
Xing Liang;Tao Zhou
利用无界区域中的反应扩散方程研究了生物物种的传播现象。当传播可以在不同的方向发生时，一个有趣的问题就产生了：哪个方向的传播最快？对于具有平流的概周期介质中的一维KPP方程：(⁎){ut=(a(X)ux)x+b(X)ux+f(x，u)t>；0，x∈R，u(0，x)=u0(X)∈[0，1]是紧支撑的非零解，设ω+和ω−分别为(⁎)在正负方向上的传播速度.上面的问题变成了这样：ω+和ω−哪个更大？本文在证明了ω+和ω−的存在性之后，完整地回答了这个问题：sgn(ω−−ω+)=sgn(Lim x→∞1 x∫0 x b(S)a(S)d S)。
Reaction-diffusion equations in unbounded domain are used to study the propagation phenomena of biological species. When propagation can happen in different directions, an interesting question arises: In which direction is propagation the fastest? For the one-dimensional KPP equation in almost periodic media with advection:(⁎){u t=(a (x) u x) x+ b (x) u x+ f (x, u) t> 0, x∈ R, u (0, x)= u 0 (x)∈[0, 1] is nonzero with compact support, let ω+ and ω− be the spreading speeds of (⁎) in the positive and negative directions respectively. The above question becomes this: Which is larger, ω+ or ω−? In this paper, after establishing the existence of ω+ and ω−, we give a complete answer to this question: sgn (ω−− ω+)= sgn (lim x→∞ 1 x∫ 0 x b (s) a (s) d s).