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Problem is to get numerical solution for equation

equ = D[c[x, y, z, t], t] - Kx * D[c[x, y, z, t], x, x] - Ky * D[c[x, y, z, t], y, y] - Kz * D[c[x, y, z, t], z, z] == 0;
c[x, y, z, t] == 0, t-> Infinity,
c[x, y, z, 0] == 0 // Assumptions -> {x != 0, y != 0, z != 0},
Integrate[Integrate[Integrate[c[x,y,z,t], {x, -Infinity, +Infinity}], {y, -Infinity, +Infinity}], {z, 0, Infinity}] == Qip

with

NDSolve[{equ,c[x, y, z, t] == 0, t-> Infinity,c[x, y, z, 0] == 0 // Assumptions -> {x != 0, y != 0, z != 0}, Integrate[Integrate[Integrate[c[x,y,z,t], {x, -Infinity, +Infinity}], {y, -Infinity, +Infinity}], {z, 0, Infinity}] == Qip}, x,y,z,t, {x,0,10}, {y,0,10}, {z,0,10}, {t, 0, 50}]

where the solution is given by

c[x_,y_,z_,t_]=Qip (4 Pi t)^1/2 exp[-1/4t (x^2/kx + y^2/ky + z^2/kz)]

and to compare with numerical

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  • $\begingroup$ Okay, it seems to be about the fundamental solution of the heat equation on $\mathbb{R}^3$ (heat kernel). This is also the fundamental solution of the advection-diffusion equation without advection (= wind?). What's not clear to me: What would you accept as numerical solution? Do you have a specific method in mind? $\endgroup$ Jun 3, 2018 at 21:09
  • $\begingroup$ Yes, you are right, it is related to the advection diffusion, the diffusivity is assumed constant in any given direction but can be different for different directions $\endgroup$
    – snezaim
    Jun 3, 2018 at 21:25
  • $\begingroup$ What is your sugestion for numerical solution? $\endgroup$
    – snezaim
    Jun 3, 2018 at 21:27
  • $\begingroup$ It will be good to plot generalised solution and to compare with numerica l solution $\endgroup$
    – snezaim
    Jun 3, 2018 at 21:31
  • $\begingroup$ I try to make question clear, please every coment is welcome $\endgroup$
    – snezaim
    Jun 11, 2018 at 7:14

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