Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation (Journal of Partial Differential Equations, 2020)
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