 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-105/1/b/iv/solution

The principal symbol is

p (τ, ξ) = τ^{2} - (1 + u^{2}) ∣ ξ ∣^{2} .

Its value on

d t

1

, independently of the data, so the initial plane is non-characteristic everywhere.

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