Direct and inverse boundary value problems for models of stationary reaction-convection-diffusion

A. I. Korotkii   ; Yu. V. Starodubtseva

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 98-113

Résumé

Direct and inverse boundary value problems for models of stationary reaction-convection-diffusion are investigated. The direct problem consists in finding a solution of the corresponding boundary value problem for given data on the boundary of the domain of the independent variable. The peculiarity of the direct problem consists in the inhomogeneity and irregularity of mixed boundary data. Solvability and stability conditions are specified for the direct problem. The inverse boundary value problem consists in finding some traces of the solution of the corresponding boundary value problem for given standard and additional data on a certain part of the boundary of the domain of the independent variable. The peculiarity of the inverse problem consists in the ill-posedness of this problem. Regularizing methods and solution algorithms are developed for the inverse problem.

Détail

Keywords: direct problem, mixed boundary condition, weak solution, stability, inverse problem, regularization, iterative methods.

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