Electron. J. Differential Equations, Vol. 2017 (2017), No. 297, pp. 1-10.

Exponential stability and blow-up for abstract nonlinear system with source terms

Peipei Wang, Jianghao Hao

Abstract:
In this article we consider an abstract nonlinear system with nonlinear source terms. We prove the exponential stability by the energy method. Also under suitable conditions on the initial values, we show that the nonlinear source terms are able to guarantee the blow-up of the solutions by convex method.

Submitted June 8, 2017. Published November 28, 2017.
Math Subject Classifications: 35L05, 35L20, 35L70, 93D15.
Key Words: Abstract nonlinear system; exponential decay; convex method; blow-up.

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Peipei Wang
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi 030006, China
email: 1576037528@qq.com
Jianghao Hao
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi 030006, China
email: hjhao@sxu.edu.cn

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