I'm an amateur in math. I have a system of nine PDE. The system is huge and I solve it numerically by an explicit finite difference scheme. The stencil I use:
One of PDE is a reaction-diffusion that creates a wave. It has a form:
\begin{align*} \frac{\partial}{\partial t}T(x,y,t)=D\Delta T(x,y,t) + R(T(x,y,t)) - F(T(x,y,t)) \end{align*}
$T(x,y,t)$ is the target function. $x,y$ are $2D$ space coordinates. $t$ is time. $R, F$ are reactions that depend on other PDE in the system.
Can I calculate how the wave of $T(x,y,t)$ is spreading? Its velocity and amplitude? I would be very grateful for a link to simple and clear materials about it.
Below is an example of waves spreading:
