So, in the show it seems Bjorn dies by the hand of Ivar. He gets the sword right through him, definitely a deadly blow, BUT there seems to be a plot twist coming up. BECAUSE – BOTH Bjorn (aka Alexander Ludvig) and HBO has been out there talking about this situation, AND personally I have the idea that these scenes on the beach is happening inside the head of Ivar.
First of all, how would Ivar get there to him, behind him? Ivar was crawling up the mountain side, and would probably not even be able to be there yet and he would most likely also be headed straight towards the town (as shown in plans in the show).
Secondly: When Alexander was asked about the whole thing his answer was: