边界耦合的非Newton渗流方程组解的临界曲线与非灭绝条件

Critical curves and non-extinction condition for non-Newtonian filtration equations coupled via boundary sources

利用上解与下解方法研究了多维空间RN中一类在边界耦合的非Newton渗流方程组,得到了方程组解的临界整体存在曲线与Fujita临界曲线.结果表明,方程组解的两种临界曲线不仅依赖于问题中的参数,而且还与空间的维数N有关,这与维数N=1时的已有结果有很大的区别.此外,还给出了该方程组解的非灭绝条件.

This paper is concerned with the critical curves and non-extinction condition of the solutions for a non-Newtonian polytropic filtration equations coupled via nonlinear boundary sources in RN. The critical global existence curve and the critical Fujita curve are given by means of various self-similar supersolutions and subsolutions. In particular, it is shown that the above two critical curves depend not only on the parameters in the problem, but also the dimension N of space. These have differs greatly from the known results for dimension N = 1. In addition, the non-extinction conditions of solutions for this problem are given.