Volume 18, Issue 4
Some Entropy Inequalities for a Quasilinear Degenerate Hyperbolic Equation

Hongjun Yuan and Xiaojing Xu

J. Part. Diff. Eq., 18 (2005), pp. 289-303.

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  • 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.

  • History

Published online: 2005-11

  • AMS Subject Headings

35L45, 35L60, 35L65

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