Abstract
<jats:p>The behavior of a defocusing semilinear integro-differential equation of hyperbolic type with zero initial conditions is investigated. By introducing a new variable and new functions, the problem is reduced to a form convenient for analysis. Using integration over characteristics, the necessary conditions for the problem data are obtained. Next, using d'Alembert's formula, the problem is reduced to solving a Volterra-type integral equation. The existence and uniqueness of a solution to this problem are proven using the contraction mapping method.</jats:p>
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Keywords
problem
using
equation
conditions
reduced
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