Abstract.
This paper is concerned with the large time behavior of traveling wave solutions to the Cauchy problem of generalized Benjamin–Bona–Mahony–Burgers equations
with prescribed initial data
Here v( > 0), β are constants, u ± are two given constants satisfying u + ≠ u − and the nonlinear function f(u) ∈C 2(R) is assumed to be either convex or concave. An algebraic time decay rate to traveling waves of the solutions of the Cauchy problem of generalized Benjamin-Bona-Mahony-Burgers equation is obtained by employing the weighted energy method developed by Kawashima and Matsumura in [6] to discuss the asymptotic behavior of traveling wave solutions to the Burgers equation.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
revised: May 23 and August 8, 2007
Rights and permissions
About this article
Cite this article
Yin, H., Chen, S. & Jin, J. Convergence rate to traveling waves for generalized Benjamin–Bona–Mahony–Burgers equations. Z. angew. Math. Phys. 59, 969–1001 (2008). https://doi.org/10.1007/s00033-007-6136-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00033-007-6136-5