I want to solve the diffusion equation on a disk centered at (0,0) with a radius of 1. I also want the flux at a radius of 0.8 to be zero. I have this initial condition at time zero:

    u[x, y, 0] == Exp[(-x^2 - y^2)/0.01] + 10*Exp[-(((x - 1)^2 + (y)^2)/0.01)]

The initial condition looks like this:

[![enter image description here][1]][1] 

The solution after time 50 looks like this:

[![enter image description here][2]][2]

The problem is that I expected because the flux is zero at radius of 0.8 then at the distance more than 0.8 from the origin the value of variable `u[x,y,t]` should be different from that of at distances shorter than 0.8. However, everything looks equilibrated.  

Here is the whole code:

    sol = NDSolveValue[{
            Laplacian[u[x, y, t], {x, y}] == D[u[x, y, t], t] + 
              NeumannValue[0., {x, y} ∈ RegionDifference[Disk[{0, 0}, 1], Disk[{0, 0}, 0.8]]],
            u[x, y, 0] == Exp[(-x^2 - y^2)/0.01] + 10*Exp[-(((x - 1)^2 + y^2)/0.01)]},
           u, {x, y} ∈ Disk[{0, 0}, 1],
           {t, 0, 50}
          ]

    Plot3D[sol[x, y, 0], {x, y} ∈ Disk[{0, 0}, 1], PlotRange -> All]

[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/PIOCO.png
  [2]: https://i.sstatic.net/OBfR0.png
  [3]: https://i.sstatic.net/G3MpQ.png