A New Approach to Equations with Memory
نویسنده
چکیده
We discuss a novel approach to the mathematical analysis of equations with memory, based on the notion of a 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→∞ G(s) > 0 we consider an abstract version of the evolution equation ∂ttu(x, t)−∆ [
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تاریخ انتشار 2009