Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems

Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems

Year:    2002

Journal of Partial Differential Equations, Vol. 15 (2002), Iss. 1 : pp. 46–68

Abstract

In this paper, we consider Cauchy problem for general first order inho- mogeneous quasilinear strictly hyperbolic systems. Under the matching condition, we first give an estimate on inhomogeneous terms. By this estimate, we obtain the asymptotic behaviour for the life-span of C¹ solutions with “slowly” decaying and small initial data and prove that the formation of singularity is due to the envelope of characteristics of the same family.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2002-JPDE-5440

Journal of Partial Differential Equations, Vol. 15 (2002), Iss. 1 : pp. 46–68

Published online:    2002-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Quasilinear hyperbolic system