白川 健

The aim of this work is to develop a simulation method focused on regional economic trend. In this light, an original model, formulated by partial differential equations, will be proposed. Consequently, the existence of time-local solutions of our mathematical model will be concluded, as a transitional report in the research.

In this paper, we consider a one-dimensional Fremond model of shape memory alloys. Let us imagine a wire of a shape memory alloy whose left-hand side is fixed, and assume that forcing terms, e.g., heat sources and external stress on the right-hand side, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we first show the existence of the global attractor for the limiting autonomous dynamical system, for instance the case of zero external stress, and secondly, characterize the asymptotic stability for nonautonomous case by the limiting global attractor.

In this paper, an evolution dynamical system, which is generated by one-dimensional Fremond models of shape memory alloys, is considered. Assuming that forcing terms converge to some time-independent terms in appropriate senses as time goes to infinity, we shall characterize the asymptotic stability for our dynamical system by the global attractor for the limiting autonomous dynamical system.