一类反应扩散方程的爆破时间下界估计

Lower Bounds of the Blow⁃Up Time for a Class of Reaction Diffusion Equations

该文讨论了一类反应项为非线性非局部热源且热汇具有时间系数的反应扩散方程,分别在Dirichlet、Neu⁃mann或Robin边界条件下,在有界区域中的爆破行为.若解可能在有限时间发生爆破,通过构造合适的辅助函数,对时间系数给出适当的条件,利用Sobolev、Hölder不等式及Payne和Schaefer积分不等式等技巧,得出了解的爆破时间下界的估计.

The blow⁃up behaviors in a bounded domain were considered for a class of reaction diffusion equations with nonlinear nonlocal heat sources and time⁃dependent⁃coefficient heat sink,under the Dirichlet,the Neumann and the Robin boundary conditions respectively.Through construction of auxiliary functions and appropriate conditions for the time⁃dependent coefficients,with the Sobolev inequality,the Hölder inequality and the Payne and Schaefer integral inequality etc.,the lower bounds of the blow⁃up time of solutions were given for the blow⁃up occurring in a finite time.