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

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.

Keywords

• Abstract nonlinear system
• exponential decay
• convex method
• blow-up