The first initial-boundary value problem for the space charge stratification equation in semiconductors

The internal and external initial-boundary value problems for 3D equation ${\frac{\partial}{\partial t}(\Delta u-u)-u=0}$ are considered. The problems are posed under the Dirichlet boundary condition on a Lyapunov surface. Using the method of dynamic potentials, the theorems of the unique existence of the solution are proved.