一类边界耦合的扩散系统爆破现象的数值模拟  

NUMERICAL SIMULATION OF BLOW-UP FOR SOME DIFFUSION SYSTEMS WITH COUPLING AT THE BOUNDARY

作　　者：江成顺[1] 姚俐[1] 李清善[2] 

机构地区：[1]信息工程大学信息工程学院,郑州450002 [2]郑州大学,郑州450052

出　　处：《计算数学》2006年第1期31-42,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(10571024);河南省高校杰出科研人才创新工程项目(2003KSCX008)资助

摘　　要：对一类边界上非平凡耦合的抛物型系统进行了数值模拟．为验证已有的关于是否出现爆破的理论成果,先用固定网格算法针对四种具体的边界条件进行试验,并根据不同的初始数据分组．为了进一步探讨爆破发生的时刻、位置以及爆破速率,再用移动网格算法针对可能出现爆破现象的两组边界条件和初始数据进行试验,并根据不同的监测函数分组．随后对算法的有效性做出说明并分析试验结果．最后对系统的一种特殊情况给出一个算例．For some diffusion systems with nontrivial coupling at the boundary, numerical simulations are performed. The problems about when and where the blow-up probably occurs and the blow-up rate are discussed. Based upon different initial data, the experiments are divided into four groups and carried on with twelve kinds of boundary parameters. For the two kinds of boundary parameters which probably lead blow-up, experiments are classified by monitor functions and performed using moving mesh methods. Then the validity of algorithms is expounded and the results of experiments are analyzed. Finally an experiment is presented for a special ~a^e.

关 键 词：扩散模型 边界耦合 爆破 数值模拟 

分 类 号：O175.26[理学—数学]