File:U(x,t)=exp(x)H(t).png

Asymptote code:

import graph3;

size(200);

real f(pair p) {
      return exp(p.x);
}

surface s = surface(f, (-1,0), (1,1), 50, 50);
draw(s, lightgray, render(compression=Low, merge=true));

xaxis3("$x$",-1,1,Arrow3);
yaxis3("$t$",-1,1,Arrow3);
zaxis3("$u$",0,Arrow3);