Hi, I have a heat equation question which I'm unsure of. The first two parts are ok, but I'll post them anyway so you have a bit of background info:
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a) Show that the solution of the heat equation with initial condition can be written as
b) Show that the solutions of the heat equation can be mapped into non-trivial solutions of Burger's equation by the Cole-Hopf transformation
and find
These are just bookwork. We get for part b).
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The next bit is the problem:
c) By taking the singular data for the heat equation construct a solution of the heat equation.
Now, I've gone through the solutions and the line has jumped from:
to
This is where I'm stuck. I'm guessing it's some kind of delta function property but I'm not sure. The threw me a little. If someone can explain what's going on, that'd be great!
Thanks.