10.6.1
We want to find the steadystate solution for the partial differential equation
α
2
u
xx
=
u
t
,
subject to the boundary conditions
u
(0
, t
) = 10,
u
(50
, t
) = 40. By definition, steadystate
means that
u
is not changing as time changes; that is
u
t
= 0. Plugging this into our PDE,
we find that
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 Fall '07
 COSTIN
 Differential Equations, Equations, Derivative, Partial differential equation, steadystate solution

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