The Cauchy problem for 1-D linear nonconservative hyperbolic systems with possibly expansive discontinuity of the coefficient: A viscous approach
- Fornet, B.
DOIAbstract
AbstractIn this paper, we consider linear nonconservative Cauchy systems with discontinuous coefficients across the noncharacteristic hypersurface {x=0}. For the sake of simplicity, we restrict ourselves to piecewise constant hyperbolic operators of the form ∂t+A(x)∂x with A(x)=A+1x>0+A−1x<0, where A±∈MN(R). Under assumptions, incorporating a sharp spectral stability assumption, we prove that a unique solution is successfully singled out by a vanishing viscosity approach. Due to our framework, which includes systems with expansive discontinuities of the coefficient, the selected small viscosity solution satisfies an unusual hyperbolic problem, which is well-posed even though it does not satisfy, in general, a Uniform Lopatinski Condition.In...
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