The Limit Behavior of Solutions for the Cauchy Problem of the Sixth-Order Boussinesq Equation
Wang H. Esfahani A.
December 2021Springer Science and Business Media B.V.
Acta Applicandae Mathematicae
2021#176Issue 1
In this work, we investigate the limit behavior as ϵ→ 0 for the solutions of the Cauchy problem of the Sixth-order Boussinesq equation utt−uxx+uxxxx−ϵuxxxxxx=(u2)xx. We show that its local solution converges to that of the Boussinesq equation utt−uxx+uxxxx=(u2)xx in C([ 0 , T] ; Hs(R) ) , s≥ 0 , as ϵ tends to 0. The ill-posedness result of Esfahani and Farah (J. Math. Anal. Appl. 385:230–242, 2012) will be here improved by proving that the associated flow map is not smooth for s< − 1.
Boussinesq equation , Dispersive limit , Initial value problem
Text of the article Перейти на текст статьи
School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, China
Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
School of Mathematics and Statistics
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026