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Volume 25, Issue 2
Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers

Shixiang Ma

DOI: 10.4208/jpde.v25.n2.4

J. Part. Diff. Eq., 25 (2012), pp. 171-186.

Published online: 2012-06

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  • Abstract

In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away fromthe shock discontinuity and the boundary at a rate of ε^1 as the viscosity ε tends to zero.

  • Keywords

Scalar viscous conservation laws inviscid limit single shock initial boundary value problem

  • AMS Subject Headings

35L65 35L67

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mashx822@gmail.com (Shixiang Ma)

  • BibTex
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  • TXT
@Article{JPDE-25-171, author = {Ma , Shixiang}, title = {Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {2}, pages = {171--186}, abstract = {

In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away fromthe shock discontinuity and the boundary at a rate of ε^1 as the viscosity ε tends to zero.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/5181.html} }
TY - JOUR T1 - Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers AU - Ma , Shixiang JO - Journal of Partial Differential Equations VL - 2 SP - 171 EP - 186 PY - 2012 DA - 2012/06 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n2.4 UR - https://global-sci.org/intro/article_detail/jpde/5181.html KW - Scalar viscous conservation laws KW - inviscid limit KW - single shock KW - initial boundary value problem AB -

In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away fromthe shock discontinuity and the boundary at a rate of ε^1 as the viscosity ε tends to zero.

Ma , Shixiang. (2012). Inviscid Limit for Scalar Viscous Conservation Laws in Presence of Strong Shocks and Boundary Layers. Journal of Partial Differential Equations. 25 (2). 171-186. doi:10.4208/jpde.v25.n2.4
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