The existence and uniqueness of forced waves in a general reaction–diffusion equation with time delay under climate change is concerned in this paper. By using upper and lower solutions method, monotone iteration scheme combined with the strong maximum principle, we show that there exists a nondecreasing and unique wave front with the speed consistent with the habitat shifting speed. Our results indicate the propagation of both the leading and trailing edges of the comoving population wavefront lag behind the climate envelope, which drives the species to extinction. Three examples and their corresponding numerical simulations are also given to illustrate the universality of analytical conclusions.

本文关注气候变化下具有时滞的一般反应扩散方程中强迫波的存在和唯一性。通过采用上下解法，单调迭代法和强最大值原理相结合，表明存在一个不递减且唯一的波阵面，其速度与生境迁移速度一致。我们的结果表明，共同移动的种群波前的前缘和后缘的传播都落后于气候包膜，这导致该物种灭绝。还给出了三个例子及其相应的数值模拟，以说明分析结论的普遍性。