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- Title
A MODEL OF VISCOELASTICITY WITH TIME-DEPENDENT MEMORY KERNELS.
- Authors
CONTI, MONICA; DANESE, VALERIA; GIORGI, CLAUDIO; PATA, VITTORINO
- Abstract
We consider the model equation arising in the theory of viscoelasticity ∂ttu-ht(0)Δu- ∫0∞ h't(s)Δu(t-s)ds+f(u) = g. Here, the main feature is that the memory kernel ht(·) 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, Duane, and Temam. 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.
- Subjects
MATHEMATICAL models of viscoelasticity; SOLID mechanics; KERNEL functions; MATHEMATICAL analysis; ANALYTIC geometry
- Publication
American Journal of Mathematics, 2018, Vol 140, Issue 2, p349
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2018.0008