Cauchy's Problem for Degenerate Quasilinear Hyperbolic Equations with Measures as Initial Values

Cauchy's Problem for Degenerate Quasilinear Hyperbolic Equations with Measures as Initial Values

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

Keywords:    Degenerate quasilinear hyperbolic equations