南通大学学报：自然科学版
南通大學學報：自然科學版
남통대학학보：자연과학판
Journal of Nantong University (Natural Science Edition)
2012年
3期
66-75
,共10页
时滞%非局部发散%渐近行为%方程
時滯%非跼部髮散%漸近行為%方程
시체%비국부발산%점근행위%방정
time delay%nonlocal dispersal%asymptotic behavior%equation
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．
首先用上、下解和單調迭代的方法研究一般的時滯非跼部髮散方程解的存在性和漸近行為．然後將這些結論運用到一類時滯的非跼部髮散方程，併且證明該方程的非負解是唯一的，且解的行為依賴方程中的參數λ，噹λ≤λ1（Ω），t→∞時解衰變至零；噹λ〉λ1（Ω），t→∞時解收斂到唯一正穩定解．另外，還證明瞭解在一定條件下爆破．
수선용상、하해화단조질대적방법연구일반적시체비국부발산방정해적존재성화점근행위．연후장저사결론운용도일류시체적비국부발산방정，병차증명해방정적비부해시유일적，차해적행위의뢰방정중적삼수λ，당λ≤λ1（Ω），t→∞시해쇠변지령；당λ〉λ1（Ω），t→∞시해수렴도유일정은정해．령외，환증명료해재일정조건하폭파．
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.
