http://ejde.math.txstate.edu/Volumes/2011/18/chen.pdf

try to enter to this link which is an article about [EXISTENCE OF SOLUTIONS FOR QUASILINEAR PARABOLIC

EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS], I have question in the page 3 section 3:

the expression:

[We need a priori estimates that permit us to extend the solution to the whole

domain [0, T].] what does it mean this expression mathematicaly?????