This preview shows pages 1–2. Sign up to view the full content.
Hint for Problem 9.24
May 9, 2011
The problem is
T
xx
+
T
yy
= sin(
ωx
)
T
(
x
= 0) =
T
(
x
=
l
) =
T
(
y
= 0) = 0
, T
(
y
→ ∞
) bounded
.
The PDE can be reduced to a homogenous one by the substitution
U
=
T
+
A
sin(
ωx
)
U
xx
=
T
xx

Aω
2
sin(
ωx
)
U
yy
=
T
yy
.
Substitute into the PDE to determine the value of
A
for it to be homogenous:
U
xx
+
Aω
2
sin(
ωx
) +
U
yy
= sin(
ωx
)
∴
A
=
ω

2
.
Now the problem becomes
U
xx
+
U
yy
= 0
U
(
x
= 0) =
ω

2
sin(
ω
0) = 0
U
(
x
=
l
) =
ω

2
sin(
ωl
)
U
(
y
= 0) =
ω

2
sin(
ωx
)
U
(
y
→ ∞
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 08/30/2011 for the course CGN 2200 taught by Professor Glagola during the Spring '11 term at University of Florida.
 Spring '11
 GLAGOLA

Click to edit the document details