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]]