The flux recovering at the ecosystem-atmosphere boundary by inverse modelling

We consider the heat and mass transfer models in the quasistationary case, i. e., all coefficients and the data of the problem depends on time while the time derivative in the equation is absent. Under consideration is the inverse problem of recovering the surface flux through the values of a solution at some collection of points lying inside the domain. The flux is sought in the form of a finite segment of the Fourier series with unknown Fourier coefficients depending on time. The problem of determining the Fourier coefficient is reduced to a system of algebraic equations with the use of special solutions to the adjoint problem. The equation is considered in a cylidrical space domain. We prove the existence and uniqueness theorems for solutions of the corresponding direct problem. The results are employed in the proof of the corresponding results for the inverse problem. The corresponding numerical algorithm in the three-dimensional case is constructed and the results of the numerical experiments are exhibited. It is demonstrated that the algorithm is stable under random perturbations of the data. The finite element method is used. The results can be used in the problem of the determination of the fluxes of green house gases from soils from the concentration measurements.