Uniqueness of solving the problem of transport and sedimentation of multicomponent suspensions in coastal systems

Abstract

The present work is devoted to the study of three-dimensional model of transport and sedimentation of suspended matter in the coastal zone. The model takes into account the following processes: advective transport due to the movement of the aquatic environment, microturbulent diffusion and gravitational sedimentation of particles of the suspension, and changes in the geometry of the bottom caused by sedimentation of the suspension or the rise of bottom sediments. The aim of the work was to conduct an analytical study of the uniqueness of the initial-boundary-value problem corresponding to the constructed model. In accordance with the stated aim, an initial-boundary-value problem is considered for a parabolic type equation with lower derivatives in the domain for which a quadratic functional is constructed and the uniqueness of the solution is proved by the energy method.