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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

snezaim
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  • 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? – Henrik Schumacher Jun 03 '18 at 21:09
  • 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 – snezaim Jun 03 '18 at 21:25
  • What is your sugestion for numerical solution? – snezaim Jun 03 '18 at 21:27
  • It will be good to plot generalised solution and to compare with numerica l solution – snezaim Jun 03 '18 at 21:31
  • I try to make question clear, please every coment is welcome – snezaim Jun 11 '18 at 07:14
  • Strongly related: https://mathematica.stackexchange.com/q/81152/1871 https://mathematica.stackexchange.com/q/71902/1871 And, your code contains a number of simple mistakes, Mathematica (OK, now it's called Wolfram) is a programming language and it has strict syntax rules, you cannot write code in such a wild way. You'd better put some effort into learning its basics first. – xzczd Jun 11 '18 at 07:34
  • Sugested relation is concered special case of this PDE Gaussian one. Thank you for coment related to the syntax, you right I ma new in this and I will try to clean all of this, but still I need help if the problem can be defined on right way in order to get numerical solution in the Wolfram Mathematica environment – snezaim Jun 11 '18 at 08:03

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