Bounds for the blow-up time a class of integro-differential problem of parabolic type with variable reaction term

Abstract

This paper is concerned with the blow-up time of the solutions to an integro-differential problem of parabolic type with variable growth if blow-up occurs. By using the differential inequality technique, we obtain lower bounds for the blow-up time and some global existence results under some conditions to variable exponent of reaction, memory kernel, and initial value.

Keywords

• Integro-differential problem
• Parabolic
• Variable reaction
• Global existence
• Blow-up
• Lower bounds