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Volume 10, Issue 4
Regularization of Solution Operators for Quasilinear Hyperbolic-parabolic Partial Differential Equations

Tai-Ping Liu

J. Part. Diff. Eq., 10 (1997), pp. 347-354.

Published online: 1997-10

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  • Abstract
We list a hierarchy of hyperbolic-parabolic partial differential equations in terms of the regularization properties of their solution operators. This ranges from the most regularizing of the heat operator to the least, that of the hyperbolic conservation laws. We illustrate this with physical examples in gas dynamics and mechanics.
  • Keywords

Nonlinear hyperbolicity dissipations conservation laws regularity of solutions

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@Article{JPDE-10-347, author = {}, title = {Regularization of Solution Operators for Quasilinear Hyperbolic-parabolic Partial Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {1997}, volume = {10}, number = {4}, pages = {347--354}, abstract = { We list a hierarchy of hyperbolic-parabolic partial differential equations in terms of the regularization properties of their solution operators. This ranges from the most regularizing of the heat operator to the least, that of the hyperbolic conservation laws. We illustrate this with physical examples in gas dynamics and mechanics.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5604.html} }
TY - JOUR T1 - Regularization of Solution Operators for Quasilinear Hyperbolic-parabolic Partial Differential Equations JO - Journal of Partial Differential Equations VL - 4 SP - 347 EP - 354 PY - 1997 DA - 1997/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5604.html KW - Nonlinear hyperbolicity KW - dissipations KW - conservation laws KW - regularity of solutions AB - We list a hierarchy of hyperbolic-parabolic partial differential equations in terms of the regularization properties of their solution operators. This ranges from the most regularizing of the heat operator to the least, that of the hyperbolic conservation laws. We illustrate this with physical examples in gas dynamics and mechanics.
Tai-Ping Liu . (2019). Regularization of Solution Operators for Quasilinear Hyperbolic-parabolic Partial Differential Equations. Journal of Partial Differential Equations. 10 (4). 347-354. doi:
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