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Volume 7, Issue 4
Blowing-Up Solutions of the Shallow Water Equations

Nurbol Koshkarbayev

DOI: 10.12150/jnma.2025.1523

J. Nonl. Mod. Anal., 7 (2025), pp. 1523-1531.

Published online: 2025-07

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

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  • Abstract

In the paper, we study the question about global unsolvability of the Kawahara and Kaup-Kupershmidt shallow water equations in a bounded domain. For certain initial-boundary-value problems of the shallow-water equations, we establish the necessary conditions for the existence of global solutions. The proof of the results is based on the nonlinear capacity method. In closing, we provide some examples.

  • Keywords

Kaup-Kupershmidt equation, Kawahara equation, shallow water, blow-up solution, mixed problem.

  • AMS Subject Headings

35K55, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1523, author = {Koshkarbayev , Nurbol}, title = {Blowing-Up Solutions of the Shallow Water Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1523--1531}, abstract = {

In the paper, we study the question about global unsolvability of the Kawahara and Kaup-Kupershmidt shallow water equations in a bounded domain. For certain initial-boundary-value problems of the shallow-water equations, we establish the necessary conditions for the existence of global solutions. The proof of the results is based on the nonlinear capacity method. In closing, we provide some examples.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1523}, url = {http://global-sci.org/intro/article_detail/jnma/24249.html} }
TY - JOUR T1 - Blowing-Up Solutions of the Shallow Water Equations AU - Koshkarbayev , Nurbol JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 1523 EP - 1531 PY - 2025 DA - 2025/07 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1523 UR - https://global-sci.org/intro/article_detail/jnma/24249.html KW - Kaup-Kupershmidt equation, Kawahara equation, shallow water, blow-up solution, mixed problem. AB -

In the paper, we study the question about global unsolvability of the Kawahara and Kaup-Kupershmidt shallow water equations in a bounded domain. For certain initial-boundary-value problems of the shallow-water equations, we establish the necessary conditions for the existence of global solutions. The proof of the results is based on the nonlinear capacity method. In closing, we provide some examples.

Koshkarbayev , Nurbol. (2025). Blowing-Up Solutions of the Shallow Water Equations. Journal of Nonlinear Modeling and Analysis. 7 (4). 1523-1531. doi:10.12150/jnma.2025.1523
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