Abstract

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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