Global solutions and blow-up for a class of strongly damped wave equations systems

Abstract

The initial-boundary value problem for semilinear wave equation systems with a strong dissipative term in bounded domain is studied. The existence of global solutions for this problem is proved by using potential well method, and the exponential decay of global solutions is given through introducing an appropriate Lyapunov function. Meanwhile, blow-up of solutions in the unstable set is also obtained.

Key words： Nonlinear wave equations systems; global solutions; exponential decay; blow-up

Acknowledgements

This research was supported by the Natural Science Foundation of Zhejiang Province (Grant No. LY17A010009).

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