Abstract
We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition
| Original language | English |
|---|---|
| Pages (from-to) | 969-987 |
| Number of pages | 19 |
| Journal | Kinetic and Related Models |
| Volume | 6 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 1 2013 |
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All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
Cite this
Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension. / Kato, Masakazu; Wang, Yu Zhu; Kawashima, Shuichi.
In: Kinetic and Related Models, Vol. 6, No. 4, 01.12.2013, p. 969-987.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension
AU - Kato, Masakazu
AU - Wang, Yu Zhu
AU - Kawashima, Shuichi
PY - 2013/12/1
Y1 - 2013/12/1
N2 - We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition
AB - We study the initial value problem for the generalized cubic double dispersion equation in one space dimension. We establish a nonlinear approximation result to our global solutions that was obtained in [6]. Moreover, we show that as time tends to infinity, the solution approaches the superposition of nonlinear diffusion waves which are given explicitly in terms of the self-similar solution of the viscous Burgers equation. The proof is based on the semigroup argument combined with the analysis of wave decomposition
UR - http://www.scopus.com/inward/record.url?scp=84888413994&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84888413994&partnerID=8YFLogxK
U2 - 10.3934/krm.2013.6.969
DO - 10.3934/krm.2013.6.969
M3 - Article
AN - SCOPUS:84888413994
VL - 6
SP - 969
EP - 987
JO - Kinetic and Related Models
JF - Kinetic and Related Models
SN - 1937-5093
IS - 4
ER -