A finite-time blow-up of a solution 
to a time-dependent differential
equation occurs when the maximal interval of classical existence has a finite
endpoint 
and a quantity needed to continue the solution becomes unbounded as 
approaches 
from below. In a common normed
space formulation, this is expressed as
 |
The relevant norm and the quantity that diverges depend on the problem; the solution itself or one of its derivatives may blow up (Galaktionov and Vázquez 2002).
For example, the solution 
of the ordinary
differential equation 
with 
blows up at 
. Finite-time blow-up is distinct from an algebraic
blow-up and a graph blow-up.
