Mathematics · Partial Differential Equations
Let u(x,t) be the solution of the initial-boundary value problem: ∂u∂t = ∂2u∂x2, u(0,t) = u(1,t) = 0, u(x,0) = 2x(1 - x). Then, which of the following statements is TRUE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1u(x,t) increases exponentially with respect to t
- 2∫01 (u(x,t))2 dx is not a decreasing function of t
- 3u(x,t) = u(1 - x, t) for all t ≥ 0 and x &invisitimes; [0,1]✓
- 40 ≤ u(x,t) ≤ 14 for all t ≥ 0 and x &invisitimes; [0,1]
Correct answer
u(x,t) = u(1 - x, t) for all t ≥ 0 and x &invisitimes; [0,1]
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