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I have to do a final project for my PDE subject and I'm looking for some interesting applications. The idea is to discuss a problem and it's related model, then possibly find a solution. I have to explain it to my teacher and my course mates in about 30-40 minutes.

Until now we have seen first order PDEs (both linear and non-linear) and second order (hyperbolic, parabolic and elliptic) PDEs. Also wave equation and heat equation.

What would be some "fun" PDE related problems to discuss? Any idea would be really appreciated! :-)

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