Since the hurricane has killed school for awhile, I was working on some stuff that I knew we would not cover in class any more, but could end up on a test and I got to this question. It seems like it should be simple, but I have been stumped all day. Don't know if anyone here will have the expertise to explain what is happening on the discontinuities. Luckily the question is an ebook; much easier to post as an image than try to type. It is Salsa's PDE's in Action, by the way, if anyone wants to see more.(adsbygoogle = window.adsbygoogle || []).push({});

So it is obvious that in each region, it is a weak (actually a strong) solution since they are constants. The problem is what happens when you pass over the discontinuities? As it is a Riemann problem with u_L < u_R, the rarefaction fan is the entropy solution we are looking for and the lines for those discontinuities have nothing to do with a RH condition. If you try to use that formula, where f(u) = 1/2*u^2, they don't match up. We are fine at 0, but when you try to show it is a weak solution across the other two lines, I can't get them to go to 0.

Anybody have some advice on how to look at this problem? It doesn't really seem to follow from what I found in the text, but maybe I missed something.

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# Proving a weak solution to PDE

Can you offer guidance or do you also need help?

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