# differential equations – Neumann's boundary condition is not satisfied I want to solve the broadcast 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 zero time:

``````    you[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: The solution after time 50 looks like this: The problem is that I was waiting for it because the flow is zero at the radius of 0.8 then at the distance greater than 0.8 of the origin the value of the variable `you[x,y,t]` should be different from distances below 0.8. However, everything seems balanced.

Here is the complete code:

``````sol = NDSolveValue[{!(
*SubsuperscriptBox[([Del]),  ({x, y} ),  (2 )

(u[x, y, t]) ) ==
re[u[u[u[u[x, y, t], t]+
NeumannValue[
0., {x, y} [Element]
RégionDifférence[Disk[{0, 0}, 1], Disc[{0, 0}, 0.8]]],
you[x, y, 0] ==
Exp[(-x^2 - y^2)/0.01] + 10 * Exp[-(((x - 1)^2 + (y)^2)/0.01)]}
u, {x, y} [Element] Disk[{0, 0}, 1], {t, 0, 50}]Plot3D[ground[ground[sol[sol[x, y, 0], {x, y} [Element] Disk[{0, 0}, 1],
PlotRange -> All]
``````  Posted on