具非局部源退化抛物型方程组的一致爆破模式

考虑带有齐次Dirichlet边界条件且具有非局部源项的退化抛物型方程组正解的爆破性质. 在适当条件下, 建立了该问题解的局部存在性并证明解在有限时刻爆破, 此外,还导出了解的两个分量同时爆破的必要条件, 并得到了该问题解的一致爆破模式.

Uniform Blow-up Properties for a Degenerate Parabolic System with Nonlocal Sources

This paper deals with the blow-up properties of positive solutions to degenerate parabolic systems with nonlocal sources, subject to null Dirichlet boundary conditions. Under appropriate hypotheses, the authors establish the local existence of the solution and the finite time blow-up. Moreover, they obtain a necessary condition for which the two components of the solution blow up simultaneously, and then establish the uniform blow-up profiles in the interior.