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Solve basic 2D heat equation with homogeneous Dirichlet BC

Posted 6 years ago

I'm a new Wolfram Mathematica user and I'm close to having Mathematica solve a basic 2D Heat Equation with Homogeneous Dirichlet BC with a given IC. I'm not sure where I am going wrong?

2D Heat Equation:

pde = D[u[x, y, t], t] - D[u[x, y, t], {x, 2}] - D[u[x, y, t] , {y, 2}] == 0

BC and IC:

ibc = {u[0, y, t] == 0, u[Pi, y, t] == 0 , u[x, 0, t] == 0, u[x, Pi, t] == 0, u[x, y, 0] == Sin[5 x] Cos[y/2]}

Domain:

\[CapitalOmega] = Rectangle[{0, 0}, {Pi, Pi}];

Attempt to Solve:

sol = DSolveValue[{pde, ibc}, 
  u[x, y, t], {x, y, t} \[Element] \[CapitalOmega]]
POSTED BY: Adam Watts

Possibly the 2D domain spec, which does not take into account the time variable.

POSTED BY: Daniel Lichtblau
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