反应扩散模型解的爆破与避免爆破

Blow-up of Solutions and Avoidance of Blow-up for Some Reaction Diffusion Models

一些动态实际应用模型,如某些反应扩散模型,在一定条件下,可能会出现解的Blow up(爆破)现象.但若能得知某一时刻将会出现Blow up现象,往往有某些特殊的办法来避免解发生Blow up.基于此,文中首先讨论了某些反应扩散模型的局部解的存在唯一性;然后利用构造辅助问题的方法和将偏微分方程转化为Volterra积分方程的技巧,给出了利用格林函数表示的模型局部解的解析表达式,在此基础上论证了模型解的爆破点集的有关性质,最后研究了相应模型如何避免解发生Blow up现象.

The actual application of some dynamic models,such as some reaction diffusion models,under certain conditions,there may be solutions of Blow up phenomenon.But when that moment will appear Blow up phenomenon,often due to some special measures to avoid the occurrence of Blow up.In view of this,at first,the author discussed the existence and uniqueness of local solutions to the corresponding reaction diffusion models.Then by using the method of constructing auxiliary problem,and the partial differential equation being transformed into Volterra integral equation techniques,the local solution of the models is given by using Green function represents.And based on the analysis of expression,the paper discussed the properties of the set for the Blow-up solutions of the models.Finally,the paper studied how to avoid the occurrence of Blow up solutions for the corresponding models.