具非局部扩散和反应项的自由边界问题  

Free boundary problems with nonlocal diffusion and reaction terms

作　　者：张羽 周玲[1] ZHANG Yu;ZHOU Ling(College of Mathematical Science,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2024年第2期73-78,共6页Journal of Yangzhou University：Natural Science Edition

基　　金：江苏自然科学基金项目(BK20191436).

摘　　要：针对一个具有非局部扩散和反应项的自由边界问题进行研究,证明其解的存在唯一性,并运用迭代法研究解的渐近行为.特别地,当扩散发生时,证明了系统存在唯一正解,且在紧开拓扑意义下全局渐近稳定,表明弱竞争时两个种群能够最终共存.In this paper,the author studies a free boundary problem with nonlocal diffusion and re-action terms,proves the existence and uniqueness of the solution,and uses iterative method to study the asymptotic behavior of the solution.In particular,when diffusion occurs,it is proved that the system has a unique positive solution and is globally asymptotically stable in the sense of com-pact expansion,indicating that two populations can eventually coexist under weak competition.

关 键 词：非局部扩散 非局部反应 自由边界条件 

分 类 号：O29[理学—应用数学] O175.2[理学—数学]