I could not plot the 3D PDE equation,

Questions
,
1

I am trying to solve this homogeneous 3D PDE, but I could not. Could you please find the problem?

new trying.nb (14.6 KB)

2

this is the IC and BC

New Doc 2020-06-21 09.20.09_1.jpg
New Doc 2020-06-21 09.20.09_1.jpg948×580 51.7 KB

3

This gives a result:

eqn = D[u[x, y, z, t], t] == 
   D[u[x, y, z, t], x, x] + D[u[x, y, z, t], y, y] + 
    D[u[x, y, z, t], z, z];
cond = {u[x, y, z, 0] == (1 - y - z) E^x,
   u[0, y, z, t] == (1 - y - z) E^t ,
   u[1, y, z, t] == (1 - y - z) E^(1 + t),
   u[x, 0, z, t] == (1 - z) E^(x + t),
   u[x, 1, z, t] == -z E^(x + t),
   u[x, y, 0, t] == (1 - y) E^(x + t),
   u[x, y, 1, t] == -y E^(x + t)};
NDSolveValue[{eqn, cond}, u,
 {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, {t, 0, 1}]
4

i could not create a plot with the command “Manipulate[
Plot3D[u[x, y, z, t] /. sol, {x, 0, 1}, {y, 0, 1} {z, 0, 1}], {t, 0,
1}]”

5

Also this command does not work.

Manipulate[
DensityPlot[u[x, y, z, t] /. sol, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, 
PlotRange -> {-1, 1}, ColorFunctionScaling -> False, 
ColorFunction -> (ColorData["TemperatureMap"][(#1 + 1)/2] &)], {t, 
0, 1}]
6

Plot3D and DensityPlot are for functions of two variables, you have three. You may try with DensityPlot3D.

7

Does not work, this command

sol = NDSolveValue[{eqn, cond}, 
  u, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, {t, 0, 1}]
Manipulate[
 Density3DPlot[u[x, y, z, t] /. sol, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, 
  PlotRange -> {-1, 1}, ColorFunctionScaling -> False, 
  ColorFunction -> (ColorData["TemperatureMap"][(#1 + 1)/2] &)], {t, 
  0, 1}]
8

It is Manipulate[DensityPlot3D[sol[x, y, z, t],...

9

I am sorry

Density3DPlot[
 u[x, y, z, t] /. sol, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, {t, 0, 1}]

also does not work.

10

This is the message

ReplaceAll::reps: {InterpolatingFunction[{{0.,1.},{0.,1.},{0.,1.},{0.,1.}},{5,5,1,{15,15,15,48},{6,6,6,4},0,0,0,0,Automatic,{},{},False},<<1>>,{Developer`PackedArrayForm,{0,5,<<47>>,245,<<161951>>},{1.,9.0072*10^15,9.0072*10^15,9.0072*10^15,1.,1.00958,9.0072*10^15,9.0072*10^15,<<35>>,9.0072*10^15,1.01911,1.0193,9.0072*10^15,9.0072*10^15,9.0072*10^15,1.01912,<<809950>>}},{Automatic,Automatic,Automatic,Automatic}]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.
11

Try DensityPlot3D. The Documentation is your reliable friend.
DensityPlot3D

12

The correct syntax is Manipulate[DensityPlot3D[sol[x, y, z, t],...

13

Than you so much Gianluca. Perfect.

14

I am try to set Flux Boundary Condition inmport at x =0 and export from Rectangular at x=1 on other face of Rectangular by using NeumannValue=u[t, X] and the other faces is closed and set NeumannValue[0] for the other faces, but it does not work.