科研之友
微信
新浪微博
Facebook
分享链接
摘要
We consider the model equation arising in the theory of viscoelasticity
partial derivative(tt)u - h(t)(0)Delta u - integral(infinity)(0) h'(t)(s)Delta u(t - s)ds + f(u) = g.
Here, the main feature is that the memory kernel h(t)(.) 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.
- 出版日期2018-4
