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I am doing a presentation in my PDE class and need ideas about topics that are interesting and either contemporary or classical. The topic needs to be something that is not covered in detail in a standard first semester PDE course, or something that is just briefly touched on (like the Gibbs phenomenon, but that's taken). Something dealing with applications to other fields would be great.

Thank you.

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    How about soliton? – 2017-02-20
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    See (for example) the lecture notes of Alessandra Lunardi, *How to use interpolation in PDE's*, Summer School on Harmonic Analysis and PDE's, Helsinki, August 2003. A different example, a model, that is this Franco Flandoli, *Elements of Mathematical Oncology* (draft). Both have the more high quality and are self contained, good luck. You can find it from the home pages of these professors. – 2017-02-20
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    When you say "PDE", do you mean a "methods"-type course where one learns to solve equations like Laplace's equation, the heat equation, and so on, or a more analysis-based course that introduces smoothness criteria, integrability and the like? – 2017-02-25

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