Mathematics · Partial Differential Equations
Let u(x, t) be the solution of the initial value problem: utt - uxx = e-t, x ∈ ℝ, t > 0, u(x, 0) = cos x, ut(x, 0) = 0, x ∈ ℝ. Then which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1For each x0 ∈ ℝ, there exists a t0 > 0 such that u(x0, t0) ≤ -4.
- 2For each x0 ∈ ℝ, there exists a t0 > 0 such that u(x0, t0) ≥ 4.✓
- 3For each x0 ∈ ℝ, |u(x0, t)| → 0 as t → &infty;.
- 4For each x0 ∈ ℝ, et u(x0, t) → 0 as t → &infty;.
Correct answer
For each x0 ∈ ℝ, there exists a t0 > 0 such that u(x0, t0) ≥ 4.
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