Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation

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.