Robin边界条件下耦合退化抛物方程组解的爆破现象

Blow-up of Solutions for Coupled Degenerate Parabolic Systems with Robin Boundary Conditions

考虑了模拟许多物理现象的耦合退化抛物方程组,其中方程的解在区域的边界上满足Robin边界条件.在前人工作的基础上,利用微分不等式,得到确保解全局存在的条件.在对已知数据项做出适当的限制后,如果解在有限时刻爆破,推导了爆破时间的下界.

The coupled degenerate parabolic equations which simulate many physical phenomena are considered,where the solutions of the equations satisfy Robin boundary conditions on the boundary of the region.Based on the previous work,the conditions for ensuring the global existence of the solutions are obtained by using the differential inequality.After making appropriate restrictions on the known date,if the solutions blow-up in finite time,the lower bound of the blow-up time is deduced.