Convergence rate to strong boundary layer solutions forgeneralized BBM-Burgers equations with non-convex flux

Tong Li; Hui Yin

doi:10.3934/cpaa.2014.13.835

Article Contents

2014, Volume 13, Issue 2: 835-858. Doi: 10.3934/cpaa.2014.13.835

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Convergence rate to strong boundary layer solutions for generalized BBM-Burgers equations with non-convex flux

Tong Li^1, and
Hui Yin^2,

1.
Department of Mathematics, University of Iowa, Iowa City, IA 52242
2.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074

Received: June 2013

Revised: August 2013

Published: March 2014

Abstract / Introduction Related Papers Cited by

Abstract

This paper is concerned with the initial-boundary value problem for the generalized Benjamin-Bona-Mahony-Burgers equation in the half space $R_+$ \begin{eqnarray} u_t-u_{txx}-u_{xx}+f(u)_{x}=0,\quad t>0, x\in R_+,\\ u(0,x)=u_0(x)\to u_+, \quad as \ \ x\to +\infty,\\ u(t,0)=u_b. \end{eqnarray} Here $u(t,x)$ is an unknown function of $t>0$ and $x\in R_+$, $u_+\not=u_b$ are two given constant states and the nonlinear function $f(u)$ is assumed to be a non-convex function which has one or finitely many inflection points. In this paper, we consider $u_b

Keywords:

Generalized Benjamin-Bona-Mahony-Burgers equation,
non-convex flux,
boundary layer solution,
global stability,
convergence rate.

Mathematics Subject Classification: Primary: 35Q53, 35B35; Secondary: 76B15.

Citation:

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