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

We prove a uniqueness theorem for a system of semilinear wave equations satisfying the null condition in $ℝ^{1 + 3}$ . Suppose that two global solutions with $C_{c}^{\infty}$ 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.

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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

Vol. 5, No. 3, 2023

Dongxiao Yu

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors