PDE problem : diffusion equation help

[sarahisme]

Hi all,

I am stuggling with this question ...

http://img86.imageshack.us/img86/2662/picture6fb5.png

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

http://img245.imageshack.us/img245/4544/picture7vu3.png


lol, this stuff is all quite confusing

-Sarah

 

[sarahisme]

hmm ok i tryed some more and i come up with this answer:

http://img301.imageshack.us/img301/3903/picture8cm8.png

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]

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]

hmm i can't seem to get separation of variables to work... what do you reckon for part (b)?

 

[J77]

For part (b), you need to reduce the nonhomogenous boundary condition problem to a homogeneous one.

 

[sarahisme]

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]

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: http://img227.imageshack.us/img227/7427/picture10zn8.png

so then we have to solve that pde problem? :S

 

[sarahisme]

its cool guys i worked it out! :D yay