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 - <p>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.</p>