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Topics - MikeMorris

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Home Assignment 3 / S2.3 Problem 8
« on: January 27, 2019, 06:42:08 PM »
In this question, the initial conditions are not given for $t = 0$, as we've discussed in class, but instead for $t = \frac{x^{2}}{2}$. I have no idea how to approach this. Could someone please help?

Home Assignment 2 / Home Assignment 2 Problem 2(a)
« on: January 16, 2019, 06:10:30 PM »
For this question (eqn 14) I found the characteristic curve to be $\frac{x}{y} = C$. It asks what the difference is between the cases $(x,y)\neq (0,0)$ and that the solution be continuous at (0,0). From what I understand, in the former case we can simply say the solution is any funtion of one variable, $u(x,y) = \phi (\frac{x}{y})$, on the domain $(x,y)\neq (0,0)$. In the second case, we need to pick some value for $u(0,0)$ to make it continuous, and elsewhere it's the same as the other case. Is this a sufficient explanation? It feels lacking to me. Could someone offer assistance?

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