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Inverse singularly perturbed problems of the convection-diffusion type in quadrangular curvilinear domains

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We have constructed an algorithm for the asymptotic approximation of the solutions of inverse singularly perturbed boundary-value problems of the convection-diffusion type with unknown diffusion coefficient, depending on the coordinates of a quadrangular curvilinear domain of filtration. The case of sufficient smoothness and consistency of the overdetermination, initial, and boundary conditions is considered. Unlike the construction of an algorithm for the solution of similar problems in doubly connected domains, here, in the corresponding relations, there appear corrections taking into account the influence of “lateral sources of pollution.” With the help of this algorithm, we have carried out a computer experiment, the results of which confirm the well-known fact of “strong sensitivity” of the model to assignment of the overdetermination condition. In particular, we have revealed the specific character of influence of this condition on the required diffusion coefficient depending on the filtration velocity.

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Authors and Affiliations

  1. National University of Water Management and Nature Resources Use, Rivne, Ukraine

    A. Ya. Bomba & O. A. Fursachyk

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  1. A. Ya. Bomba
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  2. O. A. Fursachyk
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 3, pp. 59–66, July–September, 2009.

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Bomba, A.Y., Fursachyk, O.A. Inverse singularly perturbed problems of the convection-diffusion type in quadrangular curvilinear domains. J Math Sci 171, 490–498 (2010). https://doi.org/10.1007/s10958-010-0152-2

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