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photomagnetic
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Homework Statement
Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems
with non-canonical boundary conditions to the canonical ones and write down the
equations in terms of the variable ˜u (do not solve them). Note that there are
infinitely many u1’s that solve each problem—try to find the simplest ones.
(a) Heat equation
ut = Uxx , x ∈ [0, l] ,
with the following boundary conditions
(a.1) u(0, t) = U(l, t) = A ,
(a.2) Ux(0, t) = 0 , U(l, t) = A ,
(a.3) U(0, t) = A , U(l, t) = B ,
(a.4) Ux(0, t) = Ux(l, t) = A ,
(a.5) Ux(0, t) = A , Ux(l, t) = B .
(b) Wave equation with dissipation and a perturbation on one end
Utt + aUt = c
2Uxx , x ∈ [0, l]
Homework Equations
The Attempt at a Solution
I am using
U1(x,t)= a(t)+(x-c).b(t)
then U(x,t)=U(tilda)(x,t)+U1(x,t)
I can find the U1's but not U(tilda)
is that enough to transform them into canonical form?
I'm googling like a mad man but no luck so far. can't find any good sources.
you don't have to answer the question but a little help would be nice.