The Calderón problem consists in recovering an unknown coefficient of a partial differential equation from boundary measurements of its solution. These measurements give rise to a highly nonlinear forward
operator. As a consequence, the development of reconstruction methods for this inverse problem is challenging, as they usually suffer from the problem of local convergence. To circumvent...
We introduce two reconstruction schemes that enable the recovery of a function in the entire Euclidean space $\mathbb{R}^n$ from local data $(u|_W, (-\Delta)^s u|_W)$, where $W$ is an arbitrarily small nonempty open set. These procedures rely crucially on the weak UCP for the fractional Laplacian.
We apply these schemes to two distinct inverse problems. Following the seminal work from...
In inverse problem research, both the mathematical foundations and the development of implementation technologies for industrial applications play essential roles. This presentation highlights two specific applications among several industrial cases, including inspection of wind turbine blades, quality control of smartphone cameras, maintenance of marine structures, and state estimation in...
This study focuses on estimating psychological parameters that influence decision-making, based on virtually collected consumer purchase data, and constructs a consumer purchasing behavior model grounded in prospect theory. A virtual shopping environment was developed in which consumers were presented with various combinations of the same product differing in expiration dates and prices,...
