Unformatted text preview: d. Sketch the solution u(x, t) for ﬁxed t.
5. Solve the initial value problem for the damped unidirectional wave equation
vt + cvx + λv = 0 v (x, 0) = F (x) where λ > 0 and F (x) is given.
6. (a) Solve the initial value problem for the inhomogeneous equation
vt + cvx = f (x, t) v (x, 0) = F (x) where f (x, t) and F (x) are speciﬁed functions.
(b) Solve this problem when f (x, t) = xt and F (x) = sin x.
7. Solve the “signaling” problem
vt + cvx = 0 v (0, t) = G(t) −∞ <t< ∞ in the region x > 0.
8. Solve the initial value problem
vt + ex vx = 0 v (x, 0) = x 9. Show that the initial value problem
ut + ux = x u(x, x) = 1 has no solution. Give a reason for the problem. 231 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
- Fall '08