一类时滞的非局部发散方程的渐近行为

Asymptotic Behavior for a Class of Nonlocal Dispersal Equations with Time Delay

首先用上、下解和单调迭代的方法研究一般的时滞非局部发散方程解的存在性和渐近行为,然后将这些结论运用到一类时滞的非局部发散方程,并且证明该方程的非负解是唯一的,且解的行为依赖方程中的参数λ,当λ≤λ1(Ω),t→∞时解衰变至零;当λ>λ1(Ω),t→∞时解收敛到唯一正稳定解.另外,还证明了解在一定条件下爆破.

The existence and asymptotic behavior of solution for a class of nonlocal dispersal equations with time delay is investigated. By means of super-subsolution method and monotone iteration, the existence and asymptotic behavior of solutions for a general nonlocal dispersal equation with time delay are studied first. Then, these results to equation are applied, which show that the nonnegative solution is unique, and the behavior of this solution depends on parameter A in equation. For λ〉λ1 （Ω）, the solution decays to zero as t→∞ ; while for λ〉λ1 （Ω）, the solution converges to the unique positive stationary solution as t→∞. In addition, the solution blows up under some conditions is presented.