Geodesic
On linearization of hyperbolic equations with integral load in the main part using an a priori estimate of their solutions
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 16-25

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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.
Keywords: hyperbolic equation, integral load, linearization.
Mots-clés : a priori estimation 
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     author = {O. L. Boziev},
     title = {On linearization of hyperbolic equations with integral load in the main part using an a priori estimate of their solutions},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {16--25},
     publisher = {mathdoc},
     number = {80},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_80_a1/}
}
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O. L. Boziev. On linearization of hyperbolic equations with integral load in the main part using an a priori estimate of their solutions. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 16-25. http://geodesic.mathdoc.fr/item/VTGU_2022_80_a1/