带有吸收项的抛物系统解的奇性分析  

A Coupled Parabolic System with Absorption Terms

作　　者：苏涵[1] 

机构地区：[1]安徽财经大学统计与应用数学学院,安徽蚌埠233030

出　　处：《衡水学院学报》2012年第4期18-20,共3页Journal of Hengshui University

基　　金：安徽财经大学校级科研项目(ACKYQ1133)

摘　　要：对一类带有吸收项的耦合的抛物系统并具有Dirichlet零边值的解的奇性进行了讨论,通过引入和系统参数有关的特征代数方程组,使得系统中所有非线性指标之间的相互作用被简洁地描述出来;借助构造合适的上下解,并结合比较原理得到了系统解整体存在和爆破的充分条件.由定理的结论可知,当系统中的反应项相对于吸收项起主要作用时,系统的解对于大初值在有限时刻爆破,相反当吸收项占优势时,系统的解整体存在.In this paper, we mainly discuss a coupled parabolic system with absorption terms, subject to homogeneous Dirichlet conditions. By introducing the characteristic algebraic system, the interaction among all the nonlinear exponents is simplified obviously. The sufficient conditions for global existence and blow-up of the system are obtained with the methods of upper and lower solutions combined with comparison theorems. From the conclusions of theorems, we see that solutions of the sys- tem blow up for the large initial data when the reaction term is the main effect, the solutions exist globally when the absorp- tion term is the main effect.

关 键 词：抛物系统 爆破 整体存在 吸收项 

分 类 号：O175.26[理学—数学]