Solution of a Singularly Perturbed Mixed Problem on the Half-Line for a Parabolic Equation with a Strong Turning Point of the Limit Operator

We study singularly perturbed problems in the presence of spectral singularities of the limit operator using S.A. Lomov’s regularization method. In particular, a regularized asymptotic solution is constructed for a singularly perturbed inhomogeneous mixed problem on the half-line for a parabolic equ...

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Bibliographic Details
Published in:Differential equations 2023-08, Vol.59 (8), p.1032-1049
Main Authors: Eliseev, A. G., Ratnikova, T. A., Shaposhnikova, D. A.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic methods
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Parabolic differential equations
Partial Differential Equations
Regularization
Singularity (mathematics)
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Summary:We study singularly perturbed problems in the presence of spectral singularities of the limit operator using S.A. Lomov’s regularization method. In particular, a regularized asymptotic solution is constructed for a singularly perturbed inhomogeneous mixed problem on the half-line for a parabolic equation with a strong turning point of the limit operator. Based on the idea of asymptotic integration of problems with unstable spectrum, it is shown how regularizing functions and additional regularizing operators should be introduced, the formalism of the regularization method for this type of singularity is described in detail, this algorithm is justified, and an asymptotic solution of any order in a small parameter is constructed.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123080037