Volume 43_1_(2022)_61-102

Stability properties of dissipative evolution equations with nonautonomous and nonlinear damping
Serge Nicaise

Abstract. In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a comparison principle. We then illustrate our abstract statements for different concrete examples, where new results are achieved. In a preliminary step, we prove some well-posedness results for some nonlinear and nonautonomous evolution equations

Rend. Mat. Appl. (7) 43 (2022) 61-102;  pdf