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    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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    https://brainmass.com/math/algebra/diffusion-equations-boundary-conditions-245255

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    Equilibrium (steady state) equation requires that:
    (1.1)
    This means that the function is a ...

    Solution Summary

    This solution is comprised of a detailed explanation to solve diffusion problem.

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