Existence Of Solutions For Initial-Boundary Value Problems Of A Class Of One-Dimensional Linear Wave Equations

In this paper,we consider the existence of solutions to the initial boundary value problem for a class of linear wave equation,in which the boundary conditions are not Dirichlet boundary conditions or Neumann boundary conditions or the third boundary conditions,but a linear combination of the derivatives of time and space terms.The boundary condition is derived from the study of subsonic flow in pipelines with friction.Firstly,we obtain the adjoint initial-boundary value problem of the original problem,give a priori estimate of the solution of the adjoint problem,and then obtain the uniqueness of the solution,so as to obtain the existence of the solution of the original problem.