BV solutions for the Cauchy problem of a quasilinear hyperbolic equation with σ-finite Borel measure and nonlinear source

The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the form ut +(um)x = up with nonnegative σ-finite Borel measures as initial conditions, where m>1, 0 < p 1 are some given real numbers. In particular, the existence of BV solutions for the above problem is obtained.  2005 Elsevier Inc. All rights reserved