Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems

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Volume 20, Issue 3

Weiwei Han

J. Part. Diff. Eq., 20 (2007), pp. 273-288.

Published online: 2007-08

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Abstract

In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.

Keywords

Inhomogeneous quasilinear hyperbolic system Cauchy problem global classical solution weak linear degeneracy matching condition

AMS Subject Headings

35L45 35L60.

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@Article{JPDE-20-273, author = {Weiwei Han }, title = {Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {3}, pages = {273--288}, abstract = { In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5308.html} }

TY - JOUR T1 - Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems AU - Weiwei Han JO - Journal of Partial Differential Equations VL - 3 SP - 273 EP - 288 PY - 2007 DA - 2007/08 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5308.html KW - Inhomogeneous quasilinear hyperbolic system KW - Cauchy problem KW - global classical solution KW - weak linear degeneracy KW - matching condition AB - In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.

Weiwei Han . (2007). Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems. Journal of Partial Differential Equations. 20 (3). 273-288. doi:

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