Volume 13, Issue 3
A New Viscous Regularization of the Riemann Problem for Burgers' Equation

Jinghua Wang & Hui Zhang

J. Part. Diff. Eq., 13 (2000), pp. 253-263.

Published online: 2000-08

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  • Abstract
This paper gives a new viscous regularization of the Riemann problem for Burgers' equation u_t + (\frac{u²}{2})_z = 0 with Riemann initial data u = u_(x ≤ 0), u = u_+(x > 0} at t = 0. The regularization is given by u_t + (\frac{u²}{2})_z = εe^tu_{zz} with appropriate initial data. The method is different from the classical method, through comparison of three viscous equations of it. Here it is also shown that the difference of the three regularizations approaches zero in appropriate integral norms depending on the data as ε → 0_+ for any given T > 0.
  • Keywords

Hyperbolic conservation law viscous regularization

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@Article{JPDE-13-253, author = {}, title = {A New Viscous Regularization of the Riemann Problem for Burgers' Equation}, journal = {Journal of Partial Differential Equations}, year = {2000}, volume = {13}, number = {3}, pages = {253--263}, abstract = { This paper gives a new viscous regularization of the Riemann problem for Burgers' equation u_t + (\frac{u²}{2})_z = 0 with Riemann initial data u = u_(x ≤ 0), u = u_+(x > 0} at t = 0. The regularization is given by u_t + (\frac{u²}{2})_z = εe^tu_{zz} with appropriate initial data. The method is different from the classical method, through comparison of three viscous equations of it. Here it is also shown that the difference of the three regularizations approaches zero in appropriate integral norms depending on the data as ε → 0_+ for any given T > 0.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5512.html} }
TY - JOUR T1 - A New Viscous Regularization of the Riemann Problem for Burgers' Equation JO - Journal of Partial Differential Equations VL - 3 SP - 253 EP - 263 PY - 2000 DA - 2000/08 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5512.html KW - Hyperbolic conservation law KW - viscous regularization AB - This paper gives a new viscous regularization of the Riemann problem for Burgers' equation u_t + (\frac{u²}{2})_z = 0 with Riemann initial data u = u_(x ≤ 0), u = u_+(x > 0} at t = 0. The regularization is given by u_t + (\frac{u²}{2})_z = εe^tu_{zz} with appropriate initial data. The method is different from the classical method, through comparison of three viscous equations of it. Here it is also shown that the difference of the three regularizations approaches zero in appropriate integral norms depending on the data as ε → 0_+ for any given T > 0.
Jinghua Wang & Hui Zhang . (2019). A New Viscous Regularization of the Riemann Problem for Burgers' Equation. Journal of Partial Differential Equations. 13 (3). 253-263. doi:
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