one-dimensional heat equation

[adlermaus]

Hi, I would like to solve the heat equation ( du(x, t)/dt = a * d^2u(x, t)/dx^2 ) with an initial gaussian function. An analytical solution would be: u_analytical(x, t) = 1/(2 * sqrt(π * a * (t - t0))) * exp(-(x)^2 / (4 * a * (t - t0))). If t0 is 0, then the initial condition would be a delta distribution, if t0 < 0 then it's a gaussian function.

So the problem to solve would be:
PDE: d/dt [u(x, t)] = a * d^2/dx^2 [u(x, t)]
initial condition: u(x, 0) = 1/(2 * sqrt(π * a * ( - t0))) * exp(-(x)^2 / (4 * a * ( - t0)))
boundarie conditions: u(x_min, t) = 1/(2 * sqrt(π * a * (t - t0))) * exp(-(x_min)^2 / (4 * a * (t - t0)))
u(x_max, t) = 1/(2 * sqrt(π * a * (t - t0))) * exp(-(x_max)^2 / (4 * a * (t - t0)))
For this problem, the analytical solution u_analytical should be unique, right? I didn't manage to get a good solution. I tried to overweight the initial/boundary conditions with "NonAdaptiveLoss", but that didn't work (attached is my code). Am I missing something? Thanks a lot in advance!

heat equation.zip