5.
v
t
+
cv
x
+
λv
=0
v
(
x,
0) =
F
(
x
)
where
λ>
0and
F
(
x
)isg
iven
.
The ODEs are
dx
dt
=
c,
dv
dt
=
−
λv
The initial condition for each:
x
(0) =
ξ,
v
(
ξ,
0) =
F
(
ξ
)
Solve the characteristic equation to get
x
=
ct
+
ξ.
Now solve the other ODE to get
v
(
x
(
t
)
,t
)=
Ke
−
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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
 BELL,D

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