Journal article
CONVERGENCE RATE TO STRONG BOUNDARY LAYER SOLUTIONS FOR GENERALIZED BBM-BURGERS EQUATIONS WITH NON-CONVEX FLUX
Communications on pure and applied analysis, Vol.13(2), pp.835-858
03/01/2014
DOI: 10.3934/cpaa.2014.13.835
Abstract
This paper is concerned with the initial-boundary value problem for the generalized Benjamin-Bona-Mahony-Burgers equation in the half space
R+
{ut - utxx - uxx + f (u)x = 0, t > 0, x is an element of R+, u(0, x) = u(0) (x) -> u(+), as x -> +infinity, (I) u(t, 0) = ub.
Here u(t, x) is an unknown function of t > 0 and x E R+, u+ ub 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 ub < u(+). For the non-degenerate case f'(u(+)) < 0, we show the existence and the global stability of strong boundary layer solution phi(x) with the above non-convex function f(u) satisfying (1 3). In this case, the corresponding algebraic convergence rate is also obtained. Our analysis is based on the space-time weighted energy method (cf. [4, 11]) combined with some delicate estimates.
Details
- Title: Subtitle
- CONVERGENCE RATE TO STRONG BOUNDARY LAYER SOLUTIONS FOR GENERALIZED BBM-BURGERS EQUATIONS WITH NON-CONVEX FLUX
- Creators
- Tong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USAHui Yin - Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
- Resource Type
- Journal article
- Publication Details
- Communications on pure and applied analysis, Vol.13(2), pp.835-858
- DOI
- 10.3934/cpaa.2014.13.835
- ISSN
- 1534-0392
- eISSN
- 1553-5258
- Publisher
- AMER INST MATHEMATICAL SCIENCES
- Number of pages
- 24
- Grant note
- Department of Mathematics in University of Iowa 10901064 / National Natural Science Foundation of China
- Language
- English
- Date published
- 03/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984241044902771
Metrics
16 Record Views