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math.AP2026
The initial-to-final inverse problem for the heat operator
Enric Alberola, Nesrine Aroua, Pedro Caro
We study an inverse problem for the heat equation in a medium that generates internal heat at a rate proportional to the heat density. The goal consists of determining the heat-gen…
math.AP2026
The initial-to-final-state inverse problem with critically-singular potentials
Manuel Cañizares, Pedro Caro, Ioannis Parissis +1
The Schrödinger equation in high dimensions describes the evolution of a quantum system. Assume that we are given the evolution map sending each initial state $f\in L^2(\mathbb{R}^…