I'm working on a heat diffusion problem,$$\frac{\partial T}{\partial t}=\vec{\nabla}\cdot\left(\kappa T^{5/2}\,\vec{\nabla}T\right)$$I know that, after discretization, the time step for the 1D case becomes,$$dt= \frac{\rho\,dx^2}{\kappa T_{max}^{5/2}}$$Does this imply/mean that the maximum wave speed is$$\frac{dx}{dt} = \frac{\kappa T_{max}^{5/2}}{\rho\,dx}$$or would I have to analyze this differently to get the wavespeed?
max speed  time discretization
finite difference;diffusion