Ubuntu 18.04 x86_64
I don't know if this is an issue in earlier versions or not.
In the old days when you hand edited /etc/resolv.conf, it was trivial to set a domain search list.
It seems that the gnome-control-center dialog provides no way to set a search list through the GUI.
It's possible to do so with hand editing or using nm-connection-editor and restarting the network connection, but the obvious GUI way doesn't work.
ProblemType: Bug
DistroRelease: Ubuntu 18.04
Package: gnome-control-center 1:3.28.1-0ubuntu1.18.04.1
ProcVersionSignature: Ubuntu 4.15.0-23.25-generic 4.15.18
Uname: Linux 4.15.0-23-generic x86_64
NonfreeKernelModules: nvidia_modeset nvidia
ApportVersion: 2.20.9-0ubuntu7.2
Architecture: amd64
CurrentDesktop: ubuntu:GNOME
Date: Mon Jun 25 17:39:46 2018
InstallationDate: Installed on 2018-06-19 (6 days ago)
InstallationMedia: Ubuntu 18.04 LTS "Bionic Beaver" - Release amd64 (20180426)
ProcEnviron:
TERM=xterm-256color
PATH=(custom, no user)
XDG_RUNTIME_DIR=<set>
LANG=en_US.UTF-8
SHELL=/bin/bash
SourcePackage: gnome-control-center
UpgradeStatus: No upgrade log present (probably fresh install)
Status changed to 'Confirmed' because the bug affects multiple users.