Exponential stability of abstract evolution equations with time delay

• DOI: 10.1007/s00028-014-0251-5
• Publication Date: 2014-10-13T08:19:00Z
• Authors: Serge Nicaise; Cristina Pignotti
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; [MATH]Mathematics [math]; 0101 mathematics; 01 natural sciences; Analysis of PDEs (math.AP)

We consider abstract semilinear evolution equations with a time delay feedback. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains this good property when a suitable smallness condition on the time delay feedback is satisfied. Some examples illustrating our abstract approach are also given.