On linearization of hyperbolic equations with integral load in the main part using an a priori estimate of their solutions

A priori estimates are established for solutions of one-dimensional inhomogeneous hyperbolic equations with an integral load in the main part, which has the form $a(s) = s^{p}$, for $p = 1$, $0.5$ and $-1$, with inhomogeneous initial and homogeneous boundary conditions. Here $s$ is the integral over the space variable of the square of the modulus of the derivative of the solution of the equation with respect to $x$. Examples of linearization of loaded equations by substituting the right-hand sides of the estimates for $a(s)$ are given.