Hi,
this here appears to work:
u[x_] := Exp[-4 (x - 1)^2];
\[Phi][x_] := Evaluate@Exp[-Integrate[u[y]/0.2, {y, 0, x}]];
f[x_, t_] :=
NIntegrate[(x - z)/
t \[Phi][z] Exp[-(x - z)^2/(
0.4 t)], {z, -\[Infinity], \[Infinity]}]/
NIntegrate[\[Phi][z] Exp[-(x - z)^2/(
0.4 t)], {z, -\[Infinity], \[Infinity]}];
appears to work. Basically you have to use numerical integration instead of symbolic integration.
Plot3D[f[x, t], {x, 1, 3}, {t, 1, 3}]
Cheers,
Marco
