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Energy decay for evolution equations with delay feedbacks

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  • Vilmos Komornik
  • Cristina Pignotti

Abstract

We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system generates an exponentially stable semigroup and that the delay damping coefficients are locally integrable in time. A step by step procedure combined with Gronwall's inequality allows us to prove the existence and uniqueness of solutions. Furthermore, under appropriate conditions we obtain exponential decay estimates.

Suggested Citation

  • Vilmos Komornik & Cristina Pignotti, 2022. "Energy decay for evolution equations with delay feedbacks," Mathematische Nachrichten, Wiley Blackwell, vol. 295(2), pages 377-394, February.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:2:p:377-394
    DOI: 10.1002/mana.201900532
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