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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.

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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