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Volume 18, Issue 4
Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation

Hongjun Yuan & Xiaojing Xu

J. Part. Diff. Eq., 18 (2005), pp. 289-303.

Published online: 2005-11

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  • Abstract

The aim of this paper is to discuss some degenerate hyperbolic equation u_t + φ(u)_x = 0, where φ ∈ C¹(R \ {0}) ∩ C²(R \ {0}) is a nondecreasing function in R, where R = (-∞, +∞). Some entropy inequalities are obtained and can be applied to study the existence of local BV solutions of the above equation with local finite measures as initial conditions.

  • Keywords

Quasilinear hyperbolic equations entropy inequality

  • AMS Subject Headings

35L45 35L60 35L65

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-18-289, author = {Hongjun Yuan and Xiaojing Xu }, title = {Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation}, journal = {Journal of Partial Differential Equations}, year = {2005}, volume = {18}, number = {4}, pages = {289--303}, abstract = {

The aim of this paper is to discuss some degenerate hyperbolic equation u_t + φ(u)_x = 0, where φ ∈ C¹(R \ {0}) ∩ C²(R \ {0}) is a nondecreasing function in R, where R = (-∞, +∞). Some entropy inequalities are obtained and can be applied to study the existence of local BV solutions of the above equation with local finite measures as initial conditions.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5364.html} }
TY - JOUR T1 - Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation AU - Hongjun Yuan & Xiaojing Xu JO - Journal of Partial Differential Equations VL - 4 SP - 289 EP - 303 PY - 2005 DA - 2005/11 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5364.html KW - Quasilinear hyperbolic equations KW - entropy inequality AB -

The aim of this paper is to discuss some degenerate hyperbolic equation u_t + φ(u)_x = 0, where φ ∈ C¹(R \ {0}) ∩ C²(R \ {0}) is a nondecreasing function in R, where R = (-∞, +∞). Some entropy inequalities are obtained and can be applied to study the existence of local BV solutions of the above equation with local finite measures as initial conditions.

Hongjun Yuan and Xiaojing Xu . (2005). Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation. Journal of Partial Differential Equations. 18 (4). 289-303. doi:
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