About one mathematical model of free-flow movement of groundwater

The paper analyzes methods for linearizing the nonlinear Boussinesq equation, which describes the one-dimensional unconfined movement of groundwater. A characteristic feature of these methods is the appearance of a nonlocal condition of the Samarsky type for the linearized equations. Particular emphasis is placed on the need for the linearized equation to preserve the most important property of the original linear equation, which reflects the finite speed of propagation of small disturbances. An effective and computer-implementable mathematical model of early forecast and groundwater dynamics is proposed, based on a mixed-type partial differential equation. Attention is drawn to the fact that in certain physical situations this problem may turn out to be incorrect in the sense of Hadamard.