Below is a problem about stability conditions that I have been struggling with it during an exam:
Find the stability conditions for
$$A\left ( \frac{\partial^2 u(x,\, y,\,t)}{\partial x^2} + \frac{\partial^2 u(x,\,y,\,t)}{\partial y^2} \right ) = \frac{\partial^2 u(x,\,t)}{\partial t^2}$$
$$0 \leq x \leq x_f , \; 0 \leq y \leq y_f ,\; 0 \leq t \leq T$$
Please help me with your ideas, Thanks in advance.