Problem #3
Part (a)
u
t
=Du
xx
+au−bu
3
x=L x
'
,t =T t
'
,u =U u
'
[
u
]
=U
[
u
t
]
=U
T
[
u
x
]
=U
L
[
u
xx
]
=U
L
2
U
T=DU
L
2
+aU −bU
3
[
D
]
=L
2
T
[
a
]
=L
T
[
b
]
=1
TU
2
ergo , u
t
=u
xx
+u−u
3
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Wrap Up Problem 2 Key for Partial Differential Equations | MTH 3326, Study notes of Differential Equations
Wrap Up Problem #2 Key Material Type: Notes; Professor: Beauregard; Class: Partial Differential Equations; Subject: Mathematics; University: Baylor University; Term: Spring 2011;
Typology: Study notes
2010/2011
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Problem # Part (a) ut=Duxx+ au−bu^3 x=L x ' ,t=T t ' ,u=U u '
[ u]=U [ u t ]=
U
T
[ ux ]=
U
L
[ uxx ]=
U
L
2 U T
=D
U
L
2 +aU^ −bU^ 3
[ D] =
L
2 T
[ a ]=
L
T
[ b] =
TU 2
ergo , ut=uxx +u−u^3