Blow-up phenomena for a class of metaparabolic equations with time dependent coeffcient

Abstract

This paper deals with the initial boundary value problem for a metaparabolic equations withtime dependent coeffcient. Under suitable conditions on initial data, a blow-up criterion which ensuresthat u cannot exist all time is given, and an upper bound for blow up time is derived. Moreover, wealso obtain a lower bound for blow-up time if blow up does occur by means of a di erential inequalitytechnique.

Keywords

• metaparabolic equations| blow up| upper bound| lower bound