alexa Mixed Initial-boundary Value Problem

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Mixed Initial-boundary Value Problem

Consider the following quasilinear hyperbolic system of balance laws in one space dimension:
            (1.1)
where L>0 is a constant; u=(u1,…., un)T is the unknown vector function of (t, x), f(u) is a given C3 vector function of u.
It is assumed that system (1.1) is strictly hyperbolic, i.e., for any given u on the domain under consideration, the Jacobian A(u) = ∇f(u) has n real distinct eigenvalues.

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