 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/5/i/solution

u_{xx}

- k^{2} u

: two integrations by parts have no boundary terms under the stated decay assumption. Time differentiation commutes with the spatial transform. Therefore

u_{tt} + 2 γ u_{t} + (γ^{2} + c^{2} k^{2}) u = 0.

For every fixed spatial wavenumber

k

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