@Article{JPDE-12-149,
author = {Hongjun Yuan },
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/},
url = {http://global-sci.org/intro/article_detail/jpde/5532.html}
}