As, I know that, when Lord Rama broke the Shiva-Bow,and for that reason Lord Parsuram came to the hall and challenge to the Lord Rama to war with him?Did they don't know each-other before that incidence they both are Visnu avatar ? anyone have some idea about it?.
There are different types of avataras - purna & avesha . Source
- purna avatara (Rama) - Lord himself
- avesha avatara : These itself are of 2 types :
Parashurama (all powers of Lord endowed within a jivatma)
Kartaviryarjuna (some powers of Lord endowed within a jivatma)
These are in decreasing order of shakti, so Rama defeated Parashuram who defeated Kartiviryarjuna.
So, yes, Parashurama realized that Rama was a purna avatar after he grabbed vishnu dhanus from him, and offered all his tapas to Rama realizing that his time was over, then went for more penance in mountains.