Applications of Mathematics

, Volume 57, Issue 3, pp 231–261 | Cite as

Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems

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Abstract

In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {(t, x): t ⩾ 0, x ⩽ 0} is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a C 1 solution and its L 1 stability with certain small initial and boundary data.

Keywords

quasilinear hyperbolic system mixed initial-boundary value problem global classical solution weak linear degeneracy matching conditon 

MSC 2010

35L50 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesHohai UniversityNanjingJiangsu, P.R.China

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