Chemical Engineering > GATE 2022 > Partial Differential Equations
The partial differential equation
∂u/∂t = (1/π²) ∂²u/∂x²
where, t ≥ 0 and x ∈ [0,1], is subjected to the following initial and boundary conditions:
u(x, 0) = sin(πx)
u(0, t) = 0
u(1, t) = 0
The value of t at which
u(0, t) = 0
u(1, t) = 0
u(0.5, t) / u(0.5, 0) = 1/e
is _________Correct : a
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