Hi,
Institutes offering PhD program in Journalism and Mass Communication (Media Management is a part of it) do invite application from time to time. One can check the eligibility criteria for the same and can apply for the program. Here I am providing two links which will give information about that. Aspirants need to keep checking the admission notice for that because seats are very limited for PhD programs and need to attain success in Entrance exam and Interview.
Links:
http://www.mcu.ac.in/Notifications/notification_phd_entrance_eligibility_relaxation_23022019.pdf
https://www.dauniv.ac.in/Admissions2019.php/GroupE/Guidelines%20for%20Ph.D.%20Admissions.pdf
I hope it helps!
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