Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems

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Volume 15, Issue 1

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 = {Shumin Li }, 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 AU - Shumin Li 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 . (2002). Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems. Journal of Partial Differential Equations. 15 (1). 46-68. doi:

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