这个式子可以用倒三角表示吗

baxiannv

\[
-\frac{\partial}{\partial x}\left(\alpha_x \frac{\partial \Phi}{\partial x}\right)-\frac{\partial}{\partial y}\left(\alpha_y \frac{\partial \Phi}{\partial y}\right)-\frac{\partial}{\partial z}\left(\alpha_z \frac{\partial \Phi}{\partial z}\right)+\beta \Phi=f
\]

Czhang271828

不知道 $\alpha_x$ 是代表 $\dfrac{\partial \alpha}{\partial x}$ 还是 $\alpha$ 在 $x$ 方向上的分量, 个人暂且当作分量吧. 那么答案是

$-\nabla\cdot (\alpha \nabla\Phi)+\beta\Phi=f$.

个人一般约定 $\nabla\Phi$ 为竖向量, $\alpha=\mathrm{diag}(\alpha_x,\alpha_y,\alpha_z)$ 为对角矩阵.

Czhang271828

这边真心建议学一下排版, 完全不麻烦的, 只要把下面这些东西粘贴到原问题里就可以了.

1. \[
2. -\dfrac{\partial}{\partial x}\left(\alpha_x\dfrac{\partial\Phi}{\partial x}\right)
3. -\dfrac{\partial}{\partial y}\left(\alpha_y\dfrac{\partial\Phi}{\partial y}\right)
4. -\dfrac{\partial}{\partial z}\left(\alpha_z\dfrac{\partial\Phi}{\partial z}\right)
5. +\beta\Phi=f.
6. \]

Copy the Code

效果

\[
-\dfrac{\partial}{\partial x}\left(\alpha_x\dfrac{\partial\Phi}{\partial x}\right)-\dfrac{\partial}{\partial y}\left(\alpha_y\dfrac{\partial\Phi}{\partial y}\right)-\dfrac{\partial}{\partial z}\left(\alpha_z\dfrac{\partial\Phi}{\partial z}\right)+\beta\Phi=f.
\]

代码和显示出的公式可以自行找规律对应起来, 论坛里应该有教程贴