Volume 15, Issue 1
Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems

Shumin Li

J. Part. Diff. Eq., 15 (2002), pp. 46-68.

Published online: 2002-02

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  • 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.

  • Keywords

Quasilinear hyperbolic system matching condition life-span weak linear degeneracy

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@Article{JPDE-15-46, author = {}, title = {Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {1}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5440.html} }
TY - JOUR T1 - Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems JO - Journal of Partial Differential Equations VL - 1 SP - 46 EP - 68 PY - 2002 DA - 2002/02 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5440.html KW - Quasilinear hyperbolic system KW - matching condition KW - life-span KW - weak linear degeneracy AB - 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.
Shumin Li . (2019). Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems. Journal of Partial Differential Equations. 15 (1). 46-68. doi:
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