Solution of Balance Equations for a Model of Fishery Depletion of the Non-Isolated Population

Abstract

The known class of models of the fishery depletion is enlarged for a case of the non-isolated population. Dynamics of the local open stock under the fishery influence is described using the balance differential equations. A depletion model for the homogeneous-by-space stock is given as a Cauchy task. Its solution was obtained using the method of the constant variation. The analogous model for the heterogeneous-by-space stock is formulated as a Neumann task with non-stationary boundary conditions. A solution of this task was obtained as the source functions.