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
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/12
Y1 - 2013/12
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
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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 -