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

Which boundary the characteristic hits

Consider the initial boundary value problem (IBVP)ut+ux=2u) u_{t} + u_{x} = 2u 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(2π,π)/u(π,2π)u(2\pi, \pi)/u(\pi, 2\pi) is

  1. A.eπe^\pi
  2. B.e(−π)e^(-\pi)
  3. C.−eπ-e^\pi✓ Correct
  4. D.−e(−π)-e^(-\pi)

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, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: A first-order quasilinear Cauchy problem with smooth data has a global smooth solution

More on this topic

The chapter behind this: First-order PDE: characteristics, Lagrange and Charpit — free to read

From Partial Differential Equations › First-order PDE: Lagrange, Charpit, characteristics

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