On the statement and solution of inverse problems in satellite meteorology

Marchuk, G. I.; Chavro, A. I.

doi:10.1515/rnam.1998.13.6.501

Cited by 3 publications

(1 citation statement)

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“…A significant amount of work belongs to scientists from the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS) and the Shirshov Institute of Oceanology of Russian Academy of Sciences (IO RAS). Research is being conducted on the development of perspective procedures and algorithms for analyzing observational data (ensemble optimal interpolation, Kalman filters, three-dimensional and four-dimensional variational analysis) [6,7]. In works [8][9][10] and others, biogeochemical transformations, hydrochemistry and rates of microbial processes in the water column, the assimilation of chemical elements by hydrobionts of various levels of trophic chains, and the influence of agriculture and industry on the state of the Black, Azov, and Caspian seas are studied.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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The article considers a non-stationary three-dimensional spatial mathematical model of biological kinetics and geochemical processes with nonlinear coefficients and source functions. Often, the step of analytical study in models of this kind is skipped. The purpose of this work is to fill this gap, which will allow for the application of numerical modeling methods to a model of biogeochemical cycles and a computational experiment that adequately reflects reality. For this model, an initial-boundary value problem is posed and its linearization is carried out; for all the desired functions, 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. To obtain inequalities that guarantee the convergence of solutions of a chain of linearized problems to the solution of the original nonlinear problems, the energy method, Gauss’s theorem, Green’s formula, and Poincaré’s inequality are used. The scientific novelty of this work lies in the proof of the convergence of solutions of a chain of linearized problems to the solution of the original nonlinear problems in the norm of the Hilbert space L2 as the time step τ tends to zero at the rate O(τ).

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