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Exact decay rates for weakly coupled systems with indirect damping by fractional memory effects

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  • Rafael Lima Oliveira
  • Higidio Portillo Oquendo
  • Celene Buriol

Abstract

This paper deals with the asymptotic behavior of a weakly coupled system of two equations in which one of them has a dissipative mechanism given by a memory term. This term depends on the fractional operator with exponent θ∈[0,1]$\theta \in [0,1]$. We show that strong solutions of the system decay polynomially with a rate that depends on both the exponent θ and wave propagation speeds. Optimal decay rates are found and the results show a surprising aspect: More regular damping does not necessarily imply a faster decay.

Suggested Citation

  • Rafael Lima Oliveira & Higidio Portillo Oquendo & Celene Buriol, 2023. "Exact decay rates for weakly coupled systems with indirect damping by fractional memory effects," Mathematische Nachrichten, Wiley Blackwell, vol. 296(10), pages 4610-4633, October.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:10:p:4610-4633
    DOI: 10.1002/mana.202100460
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