Explore the vast range of titles available.

We are concerned with the wave propagation in a homogeneous 2D or 3D membrane Ω of finite size. We assume that either the membrane is initially at rest or we know its initial shape (but not necessarily both) and its boundary is subject to a known boundary force. We address the question of estimating the needed time-dependent body force to exert on the membrane to reach a desired state at a given final time . As an additional information, we ask for the displacement on the boundary. We consider the displacement either at a single point of the boundary or on the whole boundary. First, we show the uniqueness of solution of these inverse problems under natural conditions on the final time . If, in addition, the displacement on the whole boundary is only time dependent (which means that the boundary moves with a constant speed), this condition on is removed if Ω satisfies Schiffer’s property. Second, we derive a conditional Hölder stability inequality for estimating such a time-dependent force. Third, we propose a numerical procedure based on the application of the satisfier function along with the standard Fourier expansion of the solution to the problems. Numerical tests are given to illustrate the applicability of the proposed procedure.

An inverse problem concerning a diffusion equation with source control parameter is considered. The approximation of the problem is based on the Ritz method with satisfier function. The Ritz method together with the least squares approximation (Ritz-least squares method) are utilized to reduce the inverse problem to the solution of algebraic equations. We extensively discuss the convergence of the method and finally present illustrative examples to demonstrate validity and applicability of the new technique.

We are living in a world filled with artifacts, including daily-use and durable products. In the context of sustainable consumption and production (SCP), the term “sufficiency” is an essential keyword. The concept of sufficiency is important for grasping the overall contribution of product functions to the fulfillment of human needs in terms of social sustainability. Sufficiency is also understood to be a necessary component for reducing the environmental impact of daily-use and durable products on the natural environment. Therefore, sufficiency is regarded as a key factor in promoting environmental sustainability. Generally, a product itself is not as essential as the functions it provides to the user. However, product functions have not only positive aspects that satisfy human needs, but also negative aspects that do not. Most existing methods for assessing the satisfaction of human needs are based on direct approaches, such as life satisfaction surveys, which do not take product functions into account. In the previous study, we proposed a living-sphere approach that integrates the traditional engineering design framework with Max-Neef’s framework of needs, relating product functions to fundamental human needs. In Max-Neef’s framework, a key concept is the “satisfier,” which refers to a conceptual method of satisfying universal human needs; however, this concept varies according to regional or local circumstances, such as culture, climate, and history. This study proposes a method to evaluate net sufficiency, which is the overall impact of product functions, both positive and negative, on fulfilling fundamental human needs. Through introducing not only a satisfier that fulfills but also a barrier that obstructs fundamental human needs, it is possible to comprehensively evaluate the degree to which a product’s functions fulfill such needs. Two case studies from Osaka and Hanoi were carried out independently, showing that the proposed method enables comprehensive evaluation of the net sufficiency of meeting fundamental needs in terms of the positive and negative aspects of product functions.