Diffusion Equations and Boundary Conditions
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Hello, I have a test coming up soon and I don't understand how to solve the kind of problem as given below. Please provide some explanation in the solution. Thanks in advance,
Eriko
Consider
the
diffusion
equation
€
φt = a
2
φxx + x
3
, −L ≤ x ≤ L
with
initial
condition
€
φ(x,0) =1
(i) Suppose
the
boundary
conditions
are
€
φ(−L,t) = 0 φ(L,t) = 0
Does
an
equilibrium
solution
exist?
If so,
solve
for
it.
(ii) Suppose
the
boundary
conditions
are
€
φ(−L,t) = 0 φx (L,t) = 0
Does
an
equilibrium
solution
exist?
If
so,
solve
for
it.
(iii) Suppose
the
boundary
conditions
are
€
φ(−L,t) =1 φx (L,t) = 0
Does
an
equilibrium
solution exist?
If
so,
solve
for
it.
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Equilibrium (steady state) equation requires that:
(1.1)
This means that the function is a ...
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