Blow-up criteria for modified two-component generalization of hyper-elastic rod equation

Abstract

We investigate the blow-up phenomena for the two-component generalization of hyper-elastic rod equation on the real line. We establish some blow-up criteria for system of coupled equations with density function that in one case alternates its sign and keeps its sign in another case under certain natural initial profiles. Presented results extend and specify the earlier blow-up criteria for such type system.

AMS subject classifications:

• 35B44
• 35L05
• 37K10

Keywords:

• Hyper-elastic rod equation
• blow-up
• two-component system

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by The Scientific and Technological Research Council of Turkey [1059B191900298].