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A uniqueness theorem for 3D semilinear wave equations satisfying the null condition

Dongxiao Yu

Vol. 5 (2023), No. 3, 601–641
DOI: 10.2140/paa.2023.5.601
Abstract

We prove a uniqueness theorem for a system of semilinear wave equations satisfying the null condition in 1+3. Suppose that two global solutions with Cc initial data have equal initial data outside a ball and equal radiation fields outside a light cone. We show that these two solutions are equal either outside a hyperboloid or everywhere in the spacetime, depending on the sizes of the ball and the light cone.

Keywords
semilinear wave equations, null condition, Friedlander radiation field, uniqueness, Carleman estimate, unique continuation
Mathematical Subject Classification
Primary: 35A02, 35L71
Milestones
Received: 13 October 2021
Revised: 28 September 2022
Accepted: 26 May 2023
Published: 24 August 2023
Authors
Dongxiao Yu
Mathematical Institute, Hausdorff Center for Mathematics
University of Bonn
Bonn
Germany