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

摘要

The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the formu(t) + (u(m))(x) = u(p)with nonnegative sigma-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. (c) 2005 Elsevier Inc. All rights reserved.