Смешанная задача для уравнения колебания ограниченной струны с производной в краевом условии, направленной не по характеристике

Abstract

The article deals with a mixed problem for the vibration equation of a finite string with a time dependent oblique derivative in the boundary condition. It’s mean that dynamic force applies to the end of a finite string. Consider a case where a derivative in the boundary condition is not directed along the characteristics. There exists a unique classical solution of the mixed problem which is represented as a restriction of some function. This function is build by special method using the results which were obtained for the solution of a problem for a semi-bounded string. The method is similar with a reflection method for the solution of a mixed problem for a finite string with fixed ends. This method has a unique nature and it is considered for the first time in the article. Formulas of the solution of this problem and matching conditions between initial and boundary conditions have been found.Получены формулы классического решения смешанной задачи.