一类半线性热传导系统解爆破的渐近行为

Asymptotic Behaviour of Blow-up for Solutions of Semilinear Heat-conductive Systems

研究半线性热传导系统 ut =uxx+λv ,vt =vxx+ku ,得出了该系统在爆破点的一个邻域内 ,当t接近有限爆破时间T <∞时 ,该系统对称解的渐近行为 ,同时用相似变量的方法得出了其增长速度 .

In this paper, the following semilinear heat-conductive systemu t=u xx+λv, v t=v xx+ku,is considered. The asymptotic behavior of symmetric solution of the system in the neighborhood of a certain blow up point is described when the time t approaches to finite blow up time T<∞. At the same time, the growth rate is obtained by using the method of similar variables.