A suspension bridges with a fractional time delay: Asymptotic behavior and Blow-up in finite time

Abstract

In the present paper, we examine a suspension bridges model subject to frictional damping, a fractional delay term, and a source term. First, we prove the existence of global solutions of the problem. Second, for small initial data, we establish the exponential stability of the system by using the energy method. Additionally, we show that if the initial energy assumes a negative value, the solution blows up in finite time.

Keywords

• suspension bridges
• fractional delay
• exponential stability
• blow-up