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Erschienen in:
2019 | OriginalPaper | Buchkapitel
5. Asymptotic Approximations for Solutions to Semilinear Elliptic and Parabolic Problems
verfasst von : Taras Mel’nyk, Dmytro Sadovyi
Erschienen in: Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2
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Abstract
Approximation techniques are demonstrated for semilinear elliptic and parabolic problems with various alternating Robin boundary conditions. With the help of special junction-layer solutions, whose behavior is determined by the type 3:2:2, and the method of matched asymptotic expansions, approximation functions are constructed for the solutions and the corresponding asymptotic estimates in Sobolev spaces are proved. These estimates show the influence of the given data and parameters on the asymptotic behavior of the solutions.