Partially Differential Equations in Tensorflow

Inspired by a course on parallel computing in my university and just after got acquainted with Tensorflow, I wrote this article as the result of a curiosity to apply framework for deep learning to the problem that has nothing to do with neural networks, but is mathematically similar.

$$\frac{\partial u}{\partial t} = \sum \limits_{\alpha=1}^{2} \frac{\partial}{\partial x_\alpha} \left (k_\alpha \frac{\partial u}{\partial x_\alpha} \right ) -u, \quad x_\alpha \in [0,1] \quad (\alpha=1,2), \ t>0;$$ $$k_\alpha = \begin{cases} 50, (x_1, x_2) \in \Delta ABC\\ 1, (x_1, x_2) \notin \Delta ABC \end{cases}$$ $$(\alpha = 1,2), \ A(0.2,0.5), \ B(0.7,0.2), \ C(0.5,0.8);$$ $$u(x_1, x_2, 0) = 0,\ u(0,x_2,t) = 1 - e^{-\omega t},\ u(1, x_2, t) = 0,$$ $$u(x_1,0,t) = 1 - e^{-\omega t},\ u(0, x_2, t) = 0,\ \omega = 20.$$

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