I was confused by the wording, so I will assume the following: the web application and the remote application are running on two different machines, with the remote application on Linux.
If that is the case, then you would be better off using a SSH library for Java (there are several - JSch, sshj, Ganymed SSH-2, to connect to the remote machine and run commands on it. This is a better approach than using ProcessBuilder, for it abstracts you from the problem of providing your password to the terminal (which can get quite tricky).
I'm not sure what you meant by this statement: "I know the application terminates automatically, so just wanted to wait for the answer." so I'll make another assumption that you want to know if the remote process terminated successfully or not. I'm unsure if any of the SSH libraries posted above, will allow you to get the remote process status in a non-trivial way, so you are better off writing a shell wrapper to your remote command that will return a parseable message.
If you are running both on the same machine, use ProcessBuilder.