Mathematics · Differential Equations
Let u = u(x, t) be the solution of the initial-boundary value problem: ∂u∂t = ∂2u∂x2, for (x, t) ∈ (0, 1) × (0, ∞) u(x, 0) = 4x(1 - x), for x ∈ [0, 1] u(0, t) = u(1, t) = 0, for t ≥ 0 Then which of the following statements is FALSE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1∫01 u(x, t)2 dx is a strictly increasing function of t✓
- 2∫01 u(x, t)2 dx is a non-increasing function of t
- 3u(x, t) = u(1 - x, t) for all x ∈ (0, 1), t > 0
- 4limt→∞ u(x, t) = 0 for all x ∈ (0, 1)
Correct answer
∫01 u(x, t)2 dx is a strictly increasing function of t
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