Part CCSIR NET June 2024which-boundary-the-characteristic-hits

Which boundary the characteristic hits

Consider the initial boundary value problem (IBVP $) u_{t} + u_{x} = 2 u$ for x > 0, t > 0; u(0, t) = 1 + sin t for t > 0; u(x, 0) = eˣ cos x for x > 0. If u is the solution of the IBVP, then the value of $u (2 π, π) / u (π, 2 π)$ is

A. $e^{π}$
B. $e^{(} - π)$
C. $- e^{π}$ ✓
D. $- e^{(} - π)$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Which boundary the characteristic hits

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