We consider a model equation arising in the theory of linear viscoelasticity. Here, the main feature is that the memory kernel depends on time, allowing for instance to describe the dynamics of aging materials. From the mathematical viewpoint, this translates into the study of dynamical systems acting on time-dependent spaces, according to the newly established theory of Di Plinio et al. [11]. In this first work, we give a proper notion of solution, and we provide a global well-posedness result. The techniques naturally extend to the analysis of the longterm behavior of the associated process, and can be exported to cover the case of general systems with memory in presence of time-dependent kernels.
A model of viscoelasticity with time-dependent memory kernels
GIORGI, Claudio;
2017-01-01
Abstract
We consider a model equation arising in the theory of linear viscoelasticity. Here, the main feature is that the memory kernel depends on time, allowing for instance to describe the dynamics of aging materials. From the mathematical viewpoint, this translates into the study of dynamical systems acting on time-dependent spaces, according to the newly established theory of Di Plinio et al. [11]. In this first work, we give a proper notion of solution, and we provide a global well-posedness result. The techniques naturally extend to the analysis of the longterm behavior of the associated process, and can be exported to cover the case of general systems with memory in presence of time-dependent kernels.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
