Counterexample to the exponential decay for systems with memory

2002 ◽  
Author(s):  
Sergio Polidoro ◽  
Keyword(s):  
Exponential Decay ◽  
Systems With Memory ◽  
With Memory

Asymptotic to systems with memory and non-local initial data

2019 ◽  
Vol 32 (05) ◽  
pp. 2050014
Author(s):  
Jaime E. Muñoz Rivera ◽  
Verónica Poblete ◽  
Juan C. Pozo ◽  
Octavio Vera
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Exponential Decay ◽  
Differential Operators ◽  
Viscoelastic System ◽  
Dissipative Case ◽  
Non Local ◽  
Systems With Memory ◽  
With Memory ◽  
Well Posed

We study the existence and the asymptotic behavior of the solution of an abstract viscoelastic system submitted to non-local initial data. [Formula: see text] [Formula: see text] where [Formula: see text] and [Formula: see text] are differential operators satisfying [Formula: see text] for [Formula: see text]. We prove that the model is well-posed. Concerning the asymptotic behavior, we show that the exponential decay holds if and only if [Formula: see text] and [Formula: see text] goes to zero exponentially. Otherwise if [Formula: see text] or the kernel goes to zero polynomially, then the solution only decays polynomially. We show the optimality of our result. Finally, we consider the non-dissipative case.

scholarly journals Parity-time symmetric systems with memory

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Zachary A. Cochran ◽  
Avadh Saxena ◽  
Yogesh N. Joglekar
Keyword(s):  
Systems With Memory ◽  
With Memory ◽  
Symmetric Systems

Relation between Anomalous and Normal Diffusion in Systems with Memory

2002 ◽  
Vol 89 (10) ◽  
Author(s):  
Rafael Morgado ◽  
Fernando A. Oliveira ◽  
G. George Batrouni ◽  
Alex Hansen
Keyword(s):  
Normal Diffusion ◽  
Systems With Memory ◽  
With Memory
Sign in / Sign up

Export Citation Format

Share Document