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- Publisher
- Springer Journals
- Copyright
- Copyright © 2019 by Springer Nature Switzerland AG
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-019-00498-5
- Publisher site
- See Article on Publisher Site
Abstract
We consider the Cauchy problem for the intermediate long-wave equation $$\begin{aligned} u_{t}-\partial _{x}u^{2}+\frac{1}{\vartheta }u_{x}+VP\int _{\mathbb {R}}\frac{1}{2\vartheta }\coth \left( \frac{\pi \left( y-x\right) }{2\vartheta }\right) u_{yy}\left( t,y\right) \mathrm{d}y=0, \end{aligned}$$ u t - ∂ x u 2 + 1 ϑ u x + V P ∫ R 1 2 ϑ coth π y - x 2 ϑ u yy t , y d y = 0 , where $$\vartheta >0$$ ϑ > 0 . Our purpose in this paper is to prove the large time asymptotic behavior of solutions under the nonzero mass condition $$\int u_{0}\left( x\right) \mathrm{d}x\ne 0$$ ∫ u 0 x d x ≠ 0 .
Journal
Journal of Evolution Equations – Springer Journals
Published: Mar 22, 2019