Global existence and blow-up of solutions for a system of Petrovsky equations

Abstract

The initial-boundary value problem for a system of Petrovsky equations with memory and nonlinear source terms in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the exponential decay estimate of global solutions. Meanwhile, under suitable conditions on relaxation functions and the positive initial energy as well as non-positive initial energy, it is proved that the solutions blow up in the finite time and the lifespan estimates of solutions are also given.

Keywords:

• Global existence
• exponential decay estimates
• blow-up
• Petrovsky systems

AMS Subject Classifications:

• 35L75
• 35B40
• 35L20

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This Research was supported by Natural Science Foundation of Zhejiang Province [grant number LY17A010009]; The National Natural Science Foundation of China [grant number 61273016]; The Public Welfare Technology Application Research Project of Zhejiang Province Science and Technology Department [grant number 2015C33088].