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 - <p style="text-align: justify;">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.</p>