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Heat kernel on a mobius band in a closed form

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128461] Heat kernel on a mobius band in a closed form
  • From: Andy <ajoshi.sipi at gmail.com>
  • Date: Mon, 22 Oct 2012 02:02:32 -0400 (EDT)
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  • Delivered-to: l-mathgroup@wolfram.com
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Hi all,
Is there a way to get a closed form expression for solution of a heat equation in closed form?
I am trying to compute the heat kernel on a mobius band in a closed form.
Here is my code:

HeatEquation = {D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}] - 
    D[u[x, y, t], {t, 1}] == 0, {u[x, y, 0] == DiracDelta[x, y],u[x,y,t]==u[-x,y+pi,t]}}
DSolve[HeatEquation, u[x, y, t], {x, y, t}]


It doesn't simplify or gives me the closed form solution.
>From the forums it seems that DSolve is probably not the correct function to do this computation but I don't know how else to go about it.
Please help.
Thanks,
Andy



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