On properties of solutions to the improved modified Boussinesq equation
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Authors
Yuzhu Wang
- School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.
Yinxia Wang
- School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China.
Abstract
In this paper, we investigate the Cauchy problem for the generalized IBq equation with damping in
one dimensional space. When \(\sigma = 1\), 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 \(\sigma\geq 2\), 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.
Share and Cite
ISRP Style
Yuzhu Wang, Yinxia Wang, On properties of solutions to the improved modified Boussinesq equation, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6004--6020
AMA Style
Wang Yuzhu, Wang Yinxia, On properties of solutions to the improved modified Boussinesq equation. J. Nonlinear Sci. Appl. (2016); 9(12):6004--6020
Chicago/Turabian Style
Wang, Yuzhu, Wang, Yinxia. "On properties of solutions to the improved modified Boussinesq equation." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6004--6020
Keywords
- IMBq equation with damping
- large time behavior
- diffusion waves.
MSC
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