Initial-boundary value problems for an equation of composite type with moving boundaries (Q1890391)

The author considers the Dirichlet problem for a composite type equation with boundary conditions formulated at the moving boundary. In certain cases the uniqueness of solution requires some additional constraints. An approximate solution is found for the equations \[ \left (\sum_{k = 0}^N a_k\frac {\partial ^k}{\partial t^k}\right )Lu = 0, \] where \(Lu\) is an operator related only to the spatial variables. As an example he investigates the two-dimensional equation of gravity-gyroscopic waves in the Boussinesq approximation and equations for ion-acoustic waves.