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- Title
The Limit Behavior of Solutions for the Cauchy Problem of the Sixth-Order Boussinesq Equation.
- Authors
Wang, Hongwei; Esfahani, Amin
- Abstract
In this work, we investigate the limit behavior as ϵ → 0 for the solutions of the Cauchy problem of the Sixth-order Boussinesq equation u t t − u x x + u x x x x − ϵ u x x x x x x = (u 2) x x . We show that its local solution converges to that of the Boussinesq equation u t t − u x x + u x x x x = (u 2) x x in C ([ 0 , T ] ; H s (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 .
- Publication
Acta Applicandae Mathematicae, 2021, Vol 176, Issue 1, p1
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-021-00458-7