YES, it is possible to make this proposal with PHP.
In fact Youtube (both YouT and other similar platforms) runs thanks to FFmpeg . And this is not to say that it is a server different from the others you use to program (except for scalability and speed, memory, etc.)
So if you're using Linux, study this powerful application (command lines and how to use it) very important, So much so that php has a native library that works with FFmpeg.
In the case of PHP think so, let's talk about your project (or idea): PHP will run on the server, then you will use to convert the files, organize, (read the stream etc) and make available to the user.
But to record, you can not with PHP or Javascript, because they are not connected to the devices of the computer (like the camera for example). So for the user to submit a video you need another question.
So everyone indicated the use of Flash, which until then was the only device that connected the camera and Microphone (do not forget it). But now there's Html5 that can also connect to these devices. Then you can send a video of your users - with Flash or Html5.
It will work, but it's worth researching in that area.
I've done something similar but only one user uploaded video to a PHP server and several user connecting live and watching. With an Adobe application called Adobe Media Live Encoder. It had a version that was free, nowadays it is paid. :
In your case it is a more daring Programming, but it's worth it.
Links:
link
- I can not post more links because it's my first time in Stack;)
