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We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the ``reduced dimensional method.'' Initially, we use the polynomial-exponential basis to approximate the inverse problem as a system of 1D nonlinear equations. We then employ a Picard iteration based on the quasi-reversibility method and a Carleman weight function. We will rigorously prove that the sequence derived from this iteration converges to the accurate solution for that 1D system without requesting a good initial guess of the true solution. The key tool for the proof is a Carleman estimate. We will also show some numerical examples. 

This paper provides a survey of the literature on the application of Multi-agent Systems (MAS) technology for Smartgrids. Smartgrids represent the next generation electric network, as communities are developing self-sufficient and environmentally friendly energy production. As a cyber-physical system, the development of the vision of Smartgrids requires the resolution of major technical problems; this has fed over a decade of research. Due to the stochastic, intermittent nature of renewable energy resources and the heterogeneity of the agents involved in a Smartgrid, demand and supply management, energy trade and control of grid elements constitute great challenges for stable operation. In addition, in order to offer resilience against faults and attacks, Smartgrids should also have restoration, self-recovery and security capabilities. Multi-agent systems (MAS) technology has been a popular approach to deal with these challenges in Smartgrids, due to their ability to support reasoning in a distributed context. This survey reviews the literature concerning the use of MAS models in each of the relevant research areas related to Smartgrids. The survey explores how researchers have utilized agent-based tools and methods to solve the main problems of Smartgrids. The survey also discusses the challenges in the advancement of Smartgrid technology and identifies the open problems for research from the view of multi-agent systems. 

This paper aims to reconstruct the initial condition of a hyperbolic equation with an unknown damping coefficient. Our approach involves approximating the hyperbolic equation’s solution by its truncated Fourier expansion in the time domain and using the recently developed polynomial-exponential basis. This truncation process facilitates the elimination of the time variable, consequently, yielding a system of quasi-linear elliptic equations. To globally solve the system without needing an accurate initial guess, we employ the Carleman contraction principle. We provide several numerical examples to illustrate the efficacy of our method. The method not only delivers precise solutions but also showcases remarkable computational efficiency. 

Abstract. Dams have proliferated along the Mekong, spurred by energy demands from economic development and capital from private companies. Swift dam evolution has rendered many databases outdated, in which mismatches arise from differing compilation methods. Without a comprehensive database, up-to-date spatial assessment of dam growth is unavailable. Looking at future development, hydropower potential specifically within the Mekong remains to be systematically evaluated. In this paper, we offer (1) an open-access and unified database of 1055 dams, (2) a spatiotemporal analysis of dams on a sub-basin and country level from the 1980s to the post-2020s, and (3) a grid-based assessment of the theoretical basin-wide hydropower potential using present-day discharge from the CaMa-Flood model (2011–2015, 0.05°) and future discharge from the WaterGAP2 model used for ISIMIP2b (2021–2040, 0.5°). The dam count of 1055 is more than twice the largest existing database, with 608 hydropower dams generating a boom in hydropower capacity from 1242 MW in the 1980s to 69 199 MW post-2020s. While China had the largest capacity increase from the 2000s to the 2010s (+16 854 MW), Laos has the most planned dams and the highest projected growth post-2020s (+18 223 MW). Based on present-day discharge, we estimate a basin-wide hydropower potential of 1 334 683 MW, where Laos is the highest at 514 887 MW. Based on future discharge modeled with climate change, hydropower potential could grow to over 2 000 000 MW. Laos and China are the highest at around 900 000 MW each, together forming over 80 % of the total potential. Our database facilitates research on dam-induced hydrological and ecological alterations, while spatiotemporal analysis of hydropower capacity could illuminate the complex transboundary electricity trade. Through both spatiotemporal and hydropower potential evaluation, we address the current and future vulnerability of countries to dam construction, highlighting the need for better planning and management in the future hydropower hotspot Laos. The Mekong dam database is publicly available at https://doi.org/10.21979/N9/ACZIJN (Ang et al., 2023).