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- Title
Exact decay rates for weakly coupled systems with indirect damping by fractional memory effects.
- Authors
Oliveira, Rafael Lima; Oquendo, Higidio Portillo; Buriol, Celene
- 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.
- Subjects
THEORY of wave motion; EXPONENTS
- Publication
Mathematische Nachrichten, 2023, Vol 296, Issue 10, p4610
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202100460