Аннотации:
Получена формула приближенного решения начально-краевой задачи
для нагруженного гиперболического уравнения, для нахождения которого
используется априорная оценка решения поставленной задачи. The article proposes a method for solving hyperbolic equation with a spatial variable integral of the
natural powers of the unknown function modulus, whereby it is loaded. The author considers an initial
boundary value problem with homogeneous boundary conditions. Scalar products of the equation by
various functionals and subsequent conversions make it possible to obtain a priori estimates of solutions
of the problem in various spaces. By successive integration over the spatial variable the reduction to an
ordinary differential equation associated with the initial one is produced. Its approximate solution is
sought using a priori estimates that are obtained. Found function leads to the formula that expresses the
approximate solution to the original problem through the right parts of the initial conditions.
Описание:
О.Л. Бозиев,
Институт информатики и проблем регионального управления
Кабардино-Балкарского научного центра РАН, г. Нальчик, Российская Федерация
E-mail: boziev@yandex.ru. O.L. Boziev
Institute of Computer Science and Problems of Regional Management of KBSC
of the Russian Academy of Sciences, Nal'chik, Russian Federation
E-mail: boziev@yandex.ru