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Volume 4, Issue 1
The Cauchy Problem for a Special System of Quasilinear Equations

Hu Jiaxin, Wang Jinghua

J. Part. Diff. Eq.,4(1991),pp.33-44

Published online: 1991-04

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  • Abstract
We have obtained in this paper the existence of weak solutions to the Cauchy problem for a special system of quasillnear equations with physical interest of the form {\frac{∂}{∂t}(u + qz) + \frac{∂}{∂x}f(u) = 0 \frac{∂z}{∂t} + kφ(u)z = 0 for the assumed smooth function φ(u) by employing the viscosity method and the theory of compensated compactness.
  • Keywords

Entropy pair weak solution

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COPYRIGHT: © Global Science Press

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@Article{JPDE-4-33, author = {Hu Jiaxin, Wang Jinghua}, title = {The Cauchy Problem for a Special System of Quasilinear Equations}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {1}, pages = {33--44}, abstract = { We have obtained in this paper the existence of weak solutions to the Cauchy problem for a special system of quasillnear equations with physical interest of the form {\frac{∂}{∂t}(u + qz) + \frac{∂}{∂x}f(u) = 0 \frac{∂z}{∂t} + kφ(u)z = 0 for the assumed smooth function φ(u) by employing the viscosity method and the theory of compensated compactness.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5759.html} }
TY - JOUR T1 - The Cauchy Problem for a Special System of Quasilinear Equations AU - Hu Jiaxin, Wang Jinghua JO - Journal of Partial Differential Equations VL - 1 SP - 33 EP - 44 PY - 1991 DA - 1991/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5759.html KW - Entropy pair KW - weak solution AB - We have obtained in this paper the existence of weak solutions to the Cauchy problem for a special system of quasillnear equations with physical interest of the form {\frac{∂}{∂t}(u + qz) + \frac{∂}{∂x}f(u) = 0 \frac{∂z}{∂t} + kφ(u)z = 0 for the assumed smooth function φ(u) by employing the viscosity method and the theory of compensated compactness.
Hu Jiaxin, Wang Jinghua. (1970). The Cauchy Problem for a Special System of Quasilinear Equations. Journal of Partial Differential Equations. 4 (1). 33-44. doi:
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