带一类时滞项的生物种群扩散模型的行波解

本文利用Schauder不动点理论证明了微分积分方程组行波解u（x，t）＝U（z）,w（x,t）＝W（z）,z＝xγ－ct的存在性．这个方程组描述了一类在植物上繁殖，且靠飞行在空中扩散的生物种群扩散过程．特别当时滞项，中积分核K（t）（反映种群繁殖模式）属于L1（0，∞）时，本文得到极限值W（－∞）（表示最终植物上种群密度）小于M．这个结论较符合生物实际．

THE TRAVELLING WAVE SOLUTION OF THE POPULATION DIFFUSION MODEL WITH A KIND OF DELAY

In this paper, the existence of the travelling wave solution $u(x,t)=U(z), w(x,t)=W(z),z=x\gamma -ct$ of the following differentic-integral equations is confirmed by the schauderfixed point theory, $$ \begin{array}{l} u_t=D\Delta u-\delta u+{w\over M}R_0\int_{-\infty}^{t}K(t-\tau)w_\tau d_\tau,\w_t=E\delta u(1-{w\over M})+(1-{w\over M})R_0\int_{-\infty}^{t}K(t-\tau)w_\tau d_\tau,\u\geq 0,\ 0\leq w< M. \end{array} $$ These equations describe the diffusion of a biological population with breeding on the plant and diffusion by flight. For the case where in the delay term $R_0\int_{-\infty}^{t}K(t-\tau)w_\tau d_\tau$ the kernel $K(t)$(the population breeding style) belongs to $L^1(0,\infty)$, it is obained that the limit $W(-\infty)$(final population density on the plant) is less than $M$. This conclusion is reasonable in bioloby.