1(a) If ut − kuxx = f, vt − kvxx = g, f ≤ g, and...

1(a) If ut − kuxx = f, vt − kvxx = g, f ≤ g, and u ≤ v at x = 0, x = l and t = 0, prove that u ≤ v for 0 ≤ x ≤ l, 0 ≤ t < ∞.

(b) If vt − vxx ≥ cos x for −π/2 ≤ x ≤ π/2, 0 < t < ∞, and if v(−π/2, t) ≥ 0, v(π/2, t) ≥ 0 and v(x, 0) ≥ cos x, use part (a) to show that v(x, t) ≥ (1 − e −t ) cos x.

Expert Solution

Colby Messinger answered 2 years ago

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