Начально-граничная задача с условиями Дирихле и Вентцеля для слабо квазилинейного биволнового уравнения

Для нестрого гиперболического слабо квазилинейного биволнового уравнения, заданного в первом квадранте, рассматривается начально-граничная задача, в которой на пространственной полупрямой заданы условия Коши, а на временной полупрямой – условия Дирихле и Вентцеля. Решение строится в неявном аналитическом виде как решение некоторых интегро-дифференциальных уравнений. Методом продолжения по параметру исследуется разрешимость этих уравнений. Для рассматриваемой задачи доказывается единственность решения и установлены условия существования ее классического решения. Если данные задачи недостаточно гладкие, то строится слабое решение.

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