We establish the existence of traveling waves for a Lotka-Volterra competition-diffusion model with a shifting habitat. It is assumed that the growth rate of each species is nondecreasing along the x-axis, positive near ∞ and negative near −∞, and shifting rightward at a speed c. We show that under appropriate conditions, for the case that one species is competitively stronger near ∞ and the case that both species coexist near ∞, there exists a critical number $\overline{c}(\infty )$ such that for any $c>\overline{c}(\infty )$ there exists a forced traveling wave with speed c connecting the origin and a semi-trivial steady state and for $c<\overline{c}(\infty )$ such a traveling wave does not exist. We also show that when a coexistence steady state exists, for any $c>0$, there is a forced traveling wave with speed c connecting the origin and the coexistence steady state.

我们为栖息地转移的Lotka-Volterra竞争扩散模型建立了行波的存在。假设每个物种的增长率沿x轴不变，在∞附近为正，在-∞附近为负，并以速度c向右移动。我们表明，在适当的条件下，对于一个物种在∞附近具有较强的竞争能力，以及两个物种在∞附近共存的情况，都存在一个临界数。$\overline{C}（\infty ）$ 这样对于任何 $C>\overline{C}（\infty ）$存在一个以速度c连接原点和半平稳态的强迫行波，并且对于$C<\overline{C}（\infty ）$这样的行波不存在。我们还表明，当存在共存稳态时，对于任何$C>0$，有一个强迫行波，速度c连接着原点和共存稳态。