Sufficient Conditions for the Existence and Uniqueness of the Solution of the Dynamics of Biogeochemical Cycles in Coastal Systems Problem

Abstract

The article considers a three-dimensional mathematical model of population dynamics based on a system of non-stationary parabolic advection-diffusion-reaction equations with lower derivatives describing the advective motion of the aquatic environment and non-linear source functions. In contrast to the previous authors’ works devoted to the description of this model and its numerical implementation, this article presents the results of an analytical study of the initial-boundary value problem corresponding to this model. For these purposes, the original initial-boundary value problem is linearized on a single time grid—for all nonlinear sources, their final spatial distributions for the previous time step are used. As a result, a chain of initial-boundary value problems is obtained, connected by initial—final data at each step of the time grid. For this chain of linearized problems, the existence and uniqueness of the solution of the initial-boundary value problem for the system of partial differential equations in the Hilbert space were researched. Numerical experiments were performed for model problems of the main types of phytoplankton populations in coastal systems under the influence of dynamically changing biotic and abiotic factors, the results of which are consistent with real physical experiments. The developed model, including the proposed model of biological kinetics, allows for the study of the productive and destructive processes of the shallow water body biocenosis to assess the state of the processes of reproduction of valuable and commercial fish participating in the food chain with selected species of summer phytoplankton.

Predicative Computing Structures and Hybrid Automates in Modeling Invasive Processes and Epidemic COVID Waves

“…The technique with hierarchical event time in the form of nested tuples is applicable in modeling the extreme development of natural processes, such as outbreaks of insect pests [ 23 ]; in the analysis of the development of the chronic course of a viral infection [ 24 ] and factors of delayed immune activation [ 25 ]; and in the study of neurogenesis [ 26 ]. It is of interest to use hybrid structures in modeling the effect of chemotaxis on the formation of dense accumulations of plankton, which is carried out in the works of Alla Nikitina using the example of monitoring the biota of the Sea of Azov [ 27 ].…”

A Model of Structural Interaction of Biophysical Factors during Invasive and Hydrological Changes in the Biosystem of the Caspian Sea

“…In the Caspian Sea, historically, it was the forage base and, accordingly, high food competition that served as a limiter for the development of fish resources [ 13 ]. Studies in the 1950s showed that, per unit of biomass of the benthic fauna of the Northern Caspian, there were several times more of its consumers than in the Sea of Azov, according to the works of Nikitina [ 14 ].…”

Research of the Solutions Proximity of Linearized and Nonlinear Problems of the Biogeochemical Process Dynamics in Coastal Systems

“…Earlier, in the article [28], the authors' team presented a description of some aspects of the construction and numerical implementation of the model of biogeochemical cycles and biological kinetics of the multispecies population model. To this end, effective numerical methods and difference schemes have been developed that allow for the simulation of biogeochemical and hydrodynamic processes in a real computational domain of a complex shape [24].…”

“…It is worth noting that the conditions for the existence and uniqueness of the solution of linearized problems were obtained earlier, along with the definition of requirements for the smoothness classes of the input data of the problem [28].…”