On properties of solutions to the improved modified Boussinesq equation

Yuzhu Wang, Yinxia Wang
2016 Journal of Nonlinear Science and its Applications  
In this paper, we investigate the Cauchy problem for the generalized IBq equation with damping in one dimensional space. When σ = 1, the nonlinear approximation of the global solutions is established under small condition on the initial value. Moreover, we show that as time tends to infinity, the solution is asymptotic to the superposition of nonlinear diffusion waves which are given explicitly in terms of the selfsimilar solution of the viscous Burgers equation. When σ ≥ 2, we prove that our
more » ... we prove that our global solution converges to the superposition of diffusion waves which are given explicitly in terms of the solution of linear parabolic equation. c 2016 all rights reserved. where s ≥ 0, 0 ≤ k ≤ s, and E 1 = f H s ∩L 1 + g H s+1 ∩L 1 . The first main purpose of this paper is to establish nonlinear approximation to global solutions to the problem (1.1), (1.2) with σ = 1. We state the result as follows.
doi:10.22436/jnsa.009.12.08 fatcat:mibina6vlvhm7lfwtq7uspnw7e