Estimates of dimension reduction errors for stationary reaction–diffusion problems

We consider the stationary reaction–diffusion model in a bounded domain $ \Omega \in {\mathbb{R}^3} $, which size along one coordinate direction is essentially smaller than along the others. By an energy type argumentation, we deduce two simplified models (zero-, and first order models) defined in a domain of the dimension two. For these models we derive estimates of the difference between the solution of the original problem and approximate solutions obtained with the help of simplified models. The right-hand sides of the estimates contain only explicitly known functions and solutions of two-dimensional problems. Bibliography: 13 titles. Illustrations: 1 figure.

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