具反应梯度项的多重非线性抛物方程解的渐近行为

Asymptotic Behavior of Solutions to a Multi-nonlinear Parabolic Equation with a Reactive Gradient Term

对一类具非线性内吸收、反应梯度项及边界流的半线性抛物方程,研究了更加困难的临界情形下的爆破解的渐近行为,填补了先前工作遗留的缺口.为此,引入了改进的伸缩变换方法.

This paper deals with a semilinear parabolic equation with nonlinear inner absorption, reactive gradient term and boundary flux. The authors consider the asymptotic behavior of the blow-up solutions in the more difficult critical situation, in order to fill a gap left by the previous work. For this purpose, some refined rescaling technique is introduced.