- #1

- 2

- 0

I'm a second year undergrad and we've covered the heat equation,

\begin{equation}

∇^{2}\Psi = \frac{1}{c^{2}}\frac{\partial^2 \Psi}{\partial t^2}

\end{equation}

and the wave equation,

\begin{equation}

D∇^{2}u= \frac{\partial u}{\partial t}

\end{equation}

in our differential equations course. Both Diffusion and wave propagation have wave like solutions, for example,

\begin{equation}

u= Ce^{-\sqrt{w/2D} x } \sin{(\sqrt{w/2D} x - wt)}

\end{equation}

\begin{equation}

\Psi = \Psi_{0} e^{i(kx-wt)}

\end{equation}

but are quite different phenomena. Could someone briefly explain the similarities/ differences in the phenomena and the solutions and how this relates to the differential equations please? Thanks.