Introduction to PDEs - quick test

Classifying PDEs

Decide whether the following systems are a boundary value problem or initial value problem, and whether they are diffusion-like, wave-like or poisson-like:

a) Brownian motion of small particles in a liquid (the random-walk)

\begin{equation} \frac{dP}{dt} = \frac{l^2}{2Np^2}\nabla^2P \end{equation}

b) the Klein-Gordon equation for describing the energy-momentum relation of relativistic particles:

\begin{equation} \left(\frac{1}{c^2}\frac{\partial^2}{\partial t^2} - \nabla^2 + \frac{m^2c^2}{\hbar^2}\right)\phi(t,x)=0 \end{equation}

Show answer

a) this is an initial value problem described by the diffusion equation
b) this is an initial value problem described by the wave equation

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See the notebook.

Back to Modelling with Partial Differential Equations.

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