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

Yong-Fu Yang — 2012

Applications of Mathematics

In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant ${(t, x) : t \geq 0, x \geq 0}$ 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.

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