Smooth and discontinuous junctions in the p-system

Rinaldo M. Colombo; Francesca Marcellini

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arXiv · 0909.1980

Smooth and discontinuous junctions in the p-system

Rinaldo M. Colombo·Francesca Marcellini

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Abstract

Consider the p-system describing the subsonic flow of a fluid in a pipe with section a = a(x). We prove that the resulting Cauchy problem generates a Lipschitz semigroup, provided the total variation of the initial datum and the oscillation of a are small. An explicit estimate on the bound of the total variation of a is provided, showing that at lower fluid speeds, higher total variations of a are acceptable. An example shows that the bound on TV(a) is mandatory, for otherwise the total variation of the solution may grow arbitrarily.

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Rinaldo M. Colombo, Francesca Marcellini. 2009-09-10. Smooth and discontinuous junctions in the p-system. https://arxiv.org/abs/0909.1980

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