# 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

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