You should have a look at multitail tool (Install using sudo apt-get install multitail
)
In short, with multitail, you need to use the --mergeall
flag for viewing output of all in one place
multitail --mergeall /var/links/proc2/id/myprocess*/Daily/myprocess*.log | grep --line-buffered "Search this: "
You can do the same without using grep
multitail -E "Search this: " --mergeall /var/links/proc2/id/myprocess*/Daily/myprocess*.log
To view the output individually using multitail, this will give the filename as well.
multitail -E "Search this: " /var/links/proc2/id/myprocess*/Daily/myprocess*.log