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Abstract
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We prove a uniqueness theorem for a system of semilinear wave equations satisfying the null condition
in . Suppose that two
global solutions with
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
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Mathematical Subject Classification
Primary: 35A02, 35L71
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Milestones
Received: 13 October 2021
Revised: 28 September 2022
Accepted: 26 May 2023
Published: 24 August 2023
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