科研之友
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摘要
We discuss a novel approach to the mathematical analysis of equations with memory, based on a new notion of state. This is the initial configuration of the system at time t = 0 which can be unambiguously determined by the knowledge of the dynamics for positive times. As a model, for a nonincreasing convex function G : R(+) R(+) such that G(0) = lim s -> 0 G(s) > lim s ->infinity G(s) > 0 we consider an abstract version of the evolution equation partial derivative(tt)u(x, t) - Delta [G(0)u(x, t) + f(0)(infinity) G'(s)u(x, t - s)ds] = 0 arising from linear viscoelasticity.
- 出版日期2010-10
