Generally, I do this command "adb shell ps" in prompt (allows to see processes running) and it's possible to discover aplication's pid. With this pid in hands, go to Eclipse and write pid:XXXX (XXXX is the application pid) then logs output is filtered by this application.
Or, in a easier way... in logcat view on Eclipse, search for any word related with your desired application, discover the pid, and then do a filter by pid "pid:XXXX".