论文标题
在与障碍物的时间分数热方程式
On the time fractional heat equation with obstacle
论文作者
论文摘要
我们研究了Caputo时间分数退化扩散方程，我们被证明等同于分数抛物线障碍物问题，表明其解决方案在（0,1）$中的任何$α\ in（0,1）$ in（0,1）$中演变为同一固定状态，即经典椭圆形问题的解决方案。 $α$变化的唯一因素是收敛速度。我们还从数值的角度研究了问题，比较了一些有限的不同方法，并显示了某些测试的结果。这些结果扩展了[1]中最近证明的情况$α= 1 $。
We study a Caputo time fractional degenerate diffusion equation which we prove to be equivalent to the fractional parabolic obstacle problem, showing that its solution evolves for any $α\in(0,1)$ to the same stationary state, the solution of the classic elliptic obstacle problem. The only thing which changes with $α$ is the convergence speed. We also study the problem from the numerical point of view, comparing some finite different approaches, and showing the results of some tests. These results extend what recently proved in [1] for the case $α=1$.
