Ideally Apache should run under its own user, like www-data. Is there a reason why you are running it as yourself?
Anyway, if you absolutely need to run it from your own user you should start it with nohup
at the end on the command . This way when you logout the system won't send a hup (hang up) signal to that process when you logout.
From the man pages:
nohup(1) - Linux man page
Name
nohup - run a command immune to hangups, with output to a non-tty
Synopsis
nohup COMMAND [ARG]...
nohup OPTION
Description
Run COMMAND, ignoring hangup signals.
--help
display this help and exit
--version
output version information and exit
If standard input is a terminal, redirect it from /dev/null. If standard output is a terminal, append output to 'nohup.out' if possible, '$HOME/nohup.out' otherwise. If standard error is a terminal, redirect it to standard output. To save output to FILE, use 'nohup COMMAND > FILE'.
NOTE: your shell may have its own version of nohup, which usually supersedes the version described here. Please refer to your shell's documentation for details about the options it supports.