PDE problem : diffusion equation! help!


by sarahisme
Tags: diffusion, equation
sarahisme
sarahisme is offline
#1
Sep27-06, 07:02 PM
P: 71
Hi all,

I am stuggling with this question ...



so far i have only tried part (a), but since i can't see how to do that so far... :(

ok so what to do...

do we first look at an 'associated problem' ? ... something like




lol, this stuff is all quite confusing

-Sarah
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sarahisme
sarahisme is offline
#2
Sep27-06, 09:24 PM
P: 71
hmm ok i tryed some more and i come up with this answer:



however i don't know how to simplify it from here, i have looked up integral tables and still no luck. any suggestions guys? lol assuming the answer is right in the first place! :P

cheers
-sarah
stunner5000pt
stunner5000pt is offline
#3
Sep28-06, 05:48 PM
P: 1,445
i think you can solve these by separation of variables that is

assume u(x,t) is a product of two functions - one which depends on x, and one which depends on t
maybe something like this u(x,t) = F(x) G(t)

and solve from there
your text should give a description of doing such a problem...

sarahisme
sarahisme is offline
#4
Sep29-06, 01:57 AM
P: 71

PDE problem : diffusion equation! help!


hmm i can't seem to get seperation of variables to work... what do you reckon for part (b)?
J77
J77 is offline
#5
Sep29-06, 02:29 AM
P: 1,157
For part (b), you need to reduce the nonhomogenous boundary condition problem to a homogeneous one.
sarahisme
sarahisme is offline
#6
Sep29-06, 03:14 AM
P: 71
Quote Quote by J77
For part (b), you need to reduce the nonhomogenous boundary condition problem to a homogeneous one.
ok, that sounds like a good idea.... but how do i go about doing that ? a hint please ;)

also, what do you think of my answer for part (a)?
sarahisme
sarahisme is offline
#7
Sep29-06, 04:11 AM
P: 71
hmm ok let me see.. what about if we let w(x,t) = exp(-x)

then u(x,t) = w(x,t) + v(x,t)

then v(x,t) satifies:

so then we have to solve that pde problem? :S
sarahisme
sarahisme is offline
#8
Sep30-06, 11:09 PM
P: 71
its cool guys i worked it out! :D yay


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