具有空变系数的混合抛物系统在非线性边界条件下解的爆破现象

Blow-up Phenomena of Mixed Parabolic Systems with Space Dependent Coefficients under Nonlinear Boundary Conditions

研究了高维空间上具有空变系数的混合抛物系统在非线性边界条件下的解的爆破问题.通过构造能量表达式,运用Sobolev不等式及其他微分不等式的技巧,得到了该能量方程所满足的微分不等式,最后积分推出了解的爆破时间下界的估计.

In our report,the blow up problem for mixed parabolic systems with space dependent coefficients under nonlinear boundary conditions in high dimensional spaces was studied. An energy expression was formulated,a Sobolev inequality and other differential inequalities were used to obtain a differential inequality which can be satisfied by the energy. Then,the lower bound estimates of blow up time were deduced.