I might have something close to what I need, but in Maple:
PDE := n*(diff(h(theta, phi, t), t)) = (diff(K*(diff(h(theta, phi, t),
theta)), theta))/(r^2*sin(phi)^2)+(diff(K*sin(phi)*(diff(h(theta, phi,
t), phi)), phi))/(r^2*sin(phi)) ;
sol := pdsolve(PDE, h(theta, phi, t));
but I...