This is more of a general question rather than anything specific but I was just wondering if someone could point me toward resources which discuss singularities in a PDE rather than in an ODE (by singularity I mean as in https://en.wikipedia.org/wiki/Singularity_(mathematics)). I did a bit of work with singularities in ODEs, but it seems working with singularities in PDEs is harder, and I can't seem to find any material on it. I have a first order PDE so it shouldn't be too difficult (I think) to work with singularities with it, but seeing as how I'm from a more probability/stats background I can't be too sure about it...
Thanks in advance.