一类高阶抛物型方程组的爆破速率估计

The Estimation of Blow-up Rate for Higher-order Parabolic Equations

摘要: 研究一类高阶抛物型偏微分方程解的爆破性质, 通过Scaling方法得出了其爆破解的爆破速率估计, 与相应常微分方程比较可知, 所得结果中爆破速率指数是最优的, 所得结果也与方程组反应项的指数为某些特殊值时前人所得结果一致。

Abstract: This paper studies the blow-up properties of higher-order parabolic partial differential equations. The author obtains the blow-up rate of blow-up solution by scaling method. The blow-up rate is optimal and consistent with the former results for the cases of some special indexes.