GATE CE 2020 Set 2 — Question 14
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Engineering Mathematics → Partial Differential Equations → 1D Diffusion Equation
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Question
The following partial differential equation is defined for The set of auxiliary conditions necessary to solve the equation uniquely, is
Correct answer
(D) one initial condition and two boundary conditions
Solution
The given equation is a parabolic partial differential equation (analogous to the 1D heat conduction equation). It is first-order with respect to the time-like variable and second-order with respect to the space-like variable . To obtain a unique solution, we require:
1.One initial condition for the first-order derivative in (e.g., ).
2.Two boundary conditions for the second-order derivative in (e.g., and ).
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