Abstract
In this paper, we consider the boundary problem for the half-strip on the plane for the case of two independent variables. This mixed problem is solved for a one-dimensional wave equation with Cauchy conditions on the basis of the half-strip and boundary conditions for lateral parts of the area border containing second-order derivatives. Moreover, the conjugation conditions are specified for the required function and its derivatives for the case when the homogeneous matching conditions are not satisfied. A classical solution to this problem is found in an analytical form by the characteristics method. This solution is approved to be unique if the relevant conditions are fulfilled.
Highlights
Заметим, что требование решения из класса дважды непрерывно дифференцируемых функций до второго порядка включительно автоматически налагает требования выполнения однородных условий согласования для заданных функций задачи
We consider the boundary problem for the half-strip on the plane for the case of two independent variables. This mixed problem is solved for a one-dimensional wave equation with Cauchy conditions on the basis of the half-strip and boundary conditions for lateral parts of the area border containing second-order derivatives
The conjugation conditions are specified for the required function and its derivatives for the case when the homogeneous matching conditions are not satisfied
Summary
Что требование решения из класса дважды непрерывно дифференцируемых функций до второго порядка включительно автоматически налагает требования выполнения однородных условий согласования для заданных функций задачи. Аналогично на этих же характеристиках можно задать условия для решения u, его производных первого порядка, условия сопряжения через заданные числа. Что условия сопряжения (6), (7) являются однородными, если все числа δ( p,k) =σ( p,k) =δ(0) =σ(0) =0 для вс= ех p 0= ,1; k 1, 2,...
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