@Article{JPDE-12-2,
author = {},
title = {Cauchy's Problem for Degenerate Quasilinear Hyperbolic Equations with Measures as Initial Values},
journal = {Journal of Partial Differential Equations},
year = {1999},
volume = {12},
number = {2},
pages = {149--178},
abstract = { The aim of this paper is to discuss the Cauchy problem for degenerate quasilinear hyperbolic equations of the form \frac{∂u}{∂t} + \frac{∂u^m}{∂x} = -u^p, m > 1, p > 0  with measures as initial conditions. The existence and uniqueness of solutions are obtained. In particular, we prove the following results: (1) 0 < p < 1 is a necessary and sufficient condition for the above equations to have extinction property; (2) 0 < p < m is a necessary and sufficient condition for the above equations to have localization property of the propagation of perturbations.},
issn = {2079-732X},
doi = {https://doi.org/1999-JPDE-5532},
url = {https://global-sci.com/article/88741/cauchys-problem-for-degenerate-quasilinear-hyperbolic-equations-with-measures-as-initial-values}
}