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Volume 5, Issue 3
Asymptotic Expansion of Solutions to Singular Perturbation Problems in Critical Cases

Hao Zhang & Na Wang

DOI: 10.12150/jnma.2023.637

J. Nonl. Mod. Anal., 5 (2023), pp. 637-647.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

This paper investigates the problem of singular perturbed integral initial values and Robin boundary values in the critical case. Based on the boundary layer function method, we not only construct the asymptotic approximation of the original equation, but also prove the uniform validity of the asymptotic solution by successive approximation. At the same time, we give an example to prove the validity of the theoretical results.

  • Keywords

Singularly perturbed problem, critical case, boundary function method, approximate solution.

  • AMS Subject Headings

34B15, 34E10, 34E15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-637, author = {Zhang , Hao and Wang , Na}, title = {Asymptotic Expansion of Solutions to Singular Perturbation Problems in Critical Cases}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {3}, pages = {637--647}, abstract = {

This paper investigates the problem of singular perturbed integral initial values and Robin boundary values in the critical case. Based on the boundary layer function method, we not only construct the asymptotic approximation of the original equation, but also prove the uniform validity of the asymptotic solution by successive approximation. At the same time, we give an example to prove the validity of the theoretical results.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.637}, url = {http://global-sci.org/intro/article_detail/jnma/21956.html} }
TY - JOUR T1 - Asymptotic Expansion of Solutions to Singular Perturbation Problems in Critical Cases AU - Zhang , Hao AU - Wang , Na JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 637 EP - 647 PY - 2023 DA - 2023/08 SN - 5 DO - http://doi.org/10.12150/jnma.2023.637 UR - https://global-sci.org/intro/article_detail/jnma/21956.html KW - Singularly perturbed problem, critical case, boundary function method, approximate solution. AB -

This paper investigates the problem of singular perturbed integral initial values and Robin boundary values in the critical case. Based on the boundary layer function method, we not only construct the asymptotic approximation of the original equation, but also prove the uniform validity of the asymptotic solution by successive approximation. At the same time, we give an example to prove the validity of the theoretical results.

Hao Zhang & Na Wang. (2023). Asymptotic Expansion of Solutions to Singular Perturbation Problems in Critical Cases. Journal of Nonlinear Modeling and Analysis. 5 (3). 637-647. doi:10.12150/jnma.2023.637
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