Characteristic boundary layers for parabolic perturbations of quasilinear hyperbolic problems |
| |
Authors: | Jing Wang Feng Xie |
| |
Institution: | a Department of Mathematics, Shanghai Normal University, ShangHai 200234, PR Chinab Department of Mathematics, Shanghai JiaoTong University, ShangHai 200240, PR Chinac The Institute of Mathematical Sciences, CUHK Shatin N.T., Hong Kong |
| |
Abstract: | In this paper, we study the existence and nonlinear stability of the totally characteristic boundary layer for the quasilinear equations with positive definite viscosity matrix under the assumption that the boundary matrix vanishes identically on the boundary x=0. We carry out a series of weighted estimates to the boundary layer equations—Prandtl type equations to get the regularity and the far field behavior of the solutions. This allows us to perform a weighted energy estimate for the error equation to prove the stability of the boundary layers. The stability result finally implies the asymptotic limit of the viscous solutions. |
| |
Keywords: | 35K20 35L50 35K60 |
本文献已被 ScienceDirect 等数据库收录! |
|