# Global behavior of solutions to an inverse problem for semilinear hyperbolic equations

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## Abstract

This paper is concerned with global in time behavior of solutions for a semilinear, hyperbolic, inverse source problem. We prove two types of results. The first one is a global nonexistence result for smooth solutions when the data is chosen appropriately. The second type of results is the asymptotic stability of solutions when the integral constraint vanishes as t goes to infinity. Bibliography: 22 titles.

## Keywords

Inverse Problem Asymptotic Stability Smooth Solution Time Behavior Hyperbolic Equation
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