Boundary layers for parabolic perturbations of quasi‐linear hyperbolic problems |
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| Authors: | Jing Wang |
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| Institution: | 1. Department of Mathematics, Shanghai Normal University, ShangHai 200234, People's Republic of China;2. The Institute of Mathematical Sciences, CUHK, Shatin, N.T., Hong Kong |
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| Abstract: | In this paper, we study the asymptotic relation between the solutions to the one‐dimensional viscous conservation laws with the Dirichlet boundary condition and the associated inviscid solution. We assume that the viscosity matrix is positive definite, then we prove the existence and the stability of the weak boundary layers by discussing nonlinear well‐posedness of the inviscid flow with certain boundary conditions. Copyright © 2009 John Wiley & Sons, Ltd. |
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| Keywords: | viscous conservation laws noncharacteristic boundary layers asymptotic analysis linearly well‐posed Lopatinski's condition nonlinear well posedness energy estimate |
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