Work

Uncertainty principles for a kinetic equation

Year: 2025

Type: article

Abstract: We study unique continuation properties for a kinetic equation. We establish sufficient conditions on the interaction potential and on the behavior of the solution at the initial and terminal times that ensure the solution is identically zero. Our strategy adapts that of Escauriaza et al. (2006), combining the logarithmic convexity of certain quantities—which yields quadratic exponential decay at infinity of the solution—with a suitable Carleman inequality, which provides a lower bound for the $ L^2 $-norm of the solution in an appropriate annular domain.

Source: Mathematical Control and Related Fields

DOI: 10.3934/mcrf.2025035

Authors: Nicola De Nitti, Minh-Binh Tran

Institutions: Texas A&M University, University of Pisa

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", Staatssekretariat für Bildung, Forschung und Innovation