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 - 2013 Dec |
| Externally published | Yes |
Keywords
- Asymptotic behavior
- Burgers equation.
- Diffusion waves
- Generalized cubic double dispersion equation
- Global existence
ASJC Scopus subject areas
- Numerical Analysis
- Modelling and Simulation