Year: 1999
Journal of Partial Differential Equations, Vol. 12 (1999), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1999-JPDE-5532
Journal of Partial Differential Equations, Vol. 12 (1999), Iss. 2 : pp. 149–178
Published online: 1999-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30