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GATE 2020 CE (CE2) – Question 14

Engineering Mathematics · PDE: Fourier series, separation of variables, diffusion, wave and Laplace equations · 1 mark · Multiple choice

For $\partial u/\partial y=\partial^2u/\partial x^2$, $y\ge0$, $x_1\le x\le x_2$, which auxiliary conditions are necessary for a unique solution?

  1. Three initial conditions
  2. Three boundary conditions
  3. Two initial conditions and one boundary condition
  4. One initial condition and two boundary conditions

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Show answer and explanation

Correct answer: (D) One initial condition and two boundary conditions

Explanation

The equation is first order in the evolution variabley,requiring one initial profileu(x,0). It is second order in spatialx,requiring conditions at the two spatial boundaries. Hence **one initial and two boundary conditions,D**.