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

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COPYRIGHT: © Global Science Press

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@Article{JPDE-18-289, author = {}, 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 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 & Xiaojing Xu . (2019). Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation. Journal of Partial Differential Equations. 18 (4). 289-303. doi:
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