Geodesic
Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems
Applications of Mathematics, Tome 57 (2012) no. 3, pp. 231-261.

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In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant $\{(t,x)\colon t \geq 0, x \geq 0\}$ 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.
DOI : 10.1007/s10492-012-0015-x
Classification : 35A01, 35A02, 35A09, 35B35, 35L50, 35L60
Keywords: quasilinear hyperbolic system; mixed initial-boundary value problem; global classical solution; weak linear degeneracy; matching conditon 
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     title = {Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems},
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Yang, Yong-Fu. Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems. Applications of Mathematics, Tome 57 (2012) no. 3, pp. 231-261. doi : 10.1007/s10492-012-0015-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0015-x/

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