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In this paper, we obtain some stability results of (abstract) dissipativeevolution equations with a nonautonomous and nonlinear damping using theexponential stability of the retrograde problem with a linear and autonomousfeedback and a comparison principle. We then illustrate our abstract statementsfor different concrete examples, where new results are achieved. In apreliminary step, we prove some well-posedness results for some nonlinear andnonautonomous evolution equations.

Stability properties of dissipative evolution equations with nonautonomous and nonlinear damping