"People who never met her or saw her – including other celebrities – are sending heartfelt messages," a Brown source tells PEOPLE of the sympathy sent out on social media following the death of Bobby and the late Whitney Houston's daughter on Sunday night. "He is cognizant of the fact that everybody is being super dope, and I think that helps him."
Brown was found facedown in the bathtub in her Atlanta-area home Jan. 31. Unconscious and unresponsive, she was transferred to various medical facilities before being moved in late June to hospice care, where the 22-year-old spent her final days.
After his daughter died, Bobby was joined by friends and family as he grieved at his home.
"He's holding up as well as can be expected," adds the source. "[Everyone is] just trying to be supportive for Bobby. Bobby's an emotional guy. That's the thing: make sure he's okay. He’s holding up well, all things considered."
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Brown's death is still under investigation and her longtime boyfriend Nick Gordon was served with a $40 million civil lawsuit by Brown's conservator.