Observation estimates for a semilinear heat equation in \mathbb{R}^n
Analysis of PDEs
2025-03-18 v1 Optimization and Control
Abstract
This paper studies the state observation problems for the semilinear heat equation in R^n. We derive observation estimates for the equation using the logarithmic convexity property of the frequency function (see [12]). As an application, we show that if two solutions coincide on a nonempty open subset \omega\subset\Omega at some time T>0, then they must be identical.
Keywords
Cite
@article{arxiv.2503.12951,
title = {Observation estimates for a semilinear heat equation in \mathbb{R}^n},
author = {Guojie Zheng and Xin Yu},
journal= {arXiv preprint arXiv:2503.12951},
year = {2025}
}