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Volume 11, Issue 2
Viscous Boundary Layers and Their Stability (I)

Zhouping Xin

J. Part. Diff. Eq., 11 (1998), pp. 97-124.

Published online: 1998-11

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  • Abstract
This paper is concerned with the asympootic limiting behavior of solutions to one-dimensional quasilinear scalar viscous equations for small viscosity in the presence of boundaries. We consider only non-characteristic boundary conditions. The main goals are to understand the evolution of viscous boundary layers, to construct the leading asymptotic ansatz which is uniformly valid up to the boundaries, and to obtain rigorously the uniform convergence to smooth solution of the associated inviscid hyperbolic equations away from the boundaries.
  • Keywords

Viscous boundary layer nonlinear stability Navier-Stokes equations compressible waves expansive wave matched asymptotic analysis

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@Article{JPDE-11-97, author = {Zhouping Xin }, title = {Viscous Boundary Layers and Their Stability (I)}, journal = {Journal of Partial Differential Equations}, year = {1998}, volume = {11}, number = {2}, pages = {97--124}, abstract = { This paper is concerned with the asympootic limiting behavior of solutions to one-dimensional quasilinear scalar viscous equations for small viscosity in the presence of boundaries. We consider only non-characteristic boundary conditions. The main goals are to understand the evolution of viscous boundary layers, to construct the leading asymptotic ansatz which is uniformly valid up to the boundaries, and to obtain rigorously the uniform convergence to smooth solution of the associated inviscid hyperbolic equations away from the boundaries.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5558.html} }
TY - JOUR T1 - Viscous Boundary Layers and Their Stability (I) AU - Zhouping Xin JO - Journal of Partial Differential Equations VL - 2 SP - 97 EP - 124 PY - 1998 DA - 1998/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5558.html KW - Viscous boundary layer KW - nonlinear stability KW - Navier-Stokes equations KW - compressible waves KW - expansive wave KW - matched asymptotic analysis AB - This paper is concerned with the asympootic limiting behavior of solutions to one-dimensional quasilinear scalar viscous equations for small viscosity in the presence of boundaries. We consider only non-characteristic boundary conditions. The main goals are to understand the evolution of viscous boundary layers, to construct the leading asymptotic ansatz which is uniformly valid up to the boundaries, and to obtain rigorously the uniform convergence to smooth solution of the associated inviscid hyperbolic equations away from the boundaries.
Zhouping Xin . (1998). Viscous Boundary Layers and Their Stability (I). Journal of Partial Differential Equations. 11 (2). 97-124. doi:
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