 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-5/1/3/c/solution

The compact support just established and

f (0) = 0

- \infty

U_{x} = u, U_{t} = - f (u), U_{t} + f (U_{x}) = 0, U (0, x) = \int_{- \infty}^{x} u_{0} (y) d y .

This is a Hamilton-Jacobi equation. There is no arbitrary function of time: the normalization at

- \infty

and the zero exterior flux determine it.

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