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- W2109733669 abstract "The well-posedness theory for hyperbolic systems of first-order quasilinear PDE's with ODE's boundary conditions (on a bounded interval) is discussed. Such systems occur in multi-scale blood flow models, as well as valveless pumping and fluid mechanics. The theory is presented in the setting of Sobolev spaces H m (m ≥ 3 being an integer), which is an appropriate set-up when it comes to proving existence of smooth solutions using energy estimates. A blow-up criterion is also derived, stating that if the maximal time of existence is finite, then the state leaves every compact subset of the hyperbolicity region, or its first-order derivatives blow-up. Finally, we discuss physical examples which fit in the general framework presented." @default.
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- W2109733669 date "2014-12-01" @default.
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- W2109733669 title "Local well-posedness of a class of hyperbolic PDE–ODE systems on a bounded interval" @default.
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- W2109733669 doi "https://doi.org/10.1142/s0219891614500222" @default.
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