Unique Continuation Properties from one time for hyperbolic Schrödinger equations

2023/06/08 by Juan Antonio Barceló, Barceló, Juan Antonio, Biagio Cassano +3 · 1 citation
Engineering · Mathematics · #35A23 #35J10 #35Q41 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.05084

openalex publication_date 2023/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we investigate properties of unique continuation for hyperbolic Schrödinger equations with time-dependent complex-valued electric fields and time-independent real magnetic fields. We show that positive masses inside of a bounded region at a single time propagate outside the region and prove gaussian lower bounds for the solutions, provided a suitable average in space-time cylinders is taken.

Cited by

• Unique continuation and Hardy's uncertainty principle for hyperbolic Schrödinger equations

Related

• Unique continuation for magnetic Schrödinger operator with singular potentials
• Mass Propagation for Electromagnetic Schrödinger Evolutions
• Uniqueness Properties of Solutions to Schrödinger Equations
• Unique continuation for the Schrodinger equation with gradient vector potentials
• Global unique continuation from a half space for the Schrödinger equation