n=10; l=10; d=0.1; tmax=3; pi=N[Pi];
zuf:=Random[Real,{-1,1}];
u=zuf+Sum[zuf Sin[2 pi i x/l],{i,n}]+
       Sum[zuf Cos[2 pi i x/l],{i,n}];
w[t_,x_]=E^t (u/.{a_ Sin[b_]->a Sin[b] Exp[-d (b/x)^2 t],
                      a_ Cos[b_]->a Cos[b] Exp[-d (b/x)^2 t]});
bild=Plot3D[w[t,x],{x,0,l},{t,0,tmax},
            AxesLabel->{"x","t","w"},ImageSize->{400,300}];