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Pré-Publication, Document De Travail Année : 2018

A note on the existence of L^2 valued solutions for a hyperbolic system with boundary conditions

Stefano Marchesani
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Résumé

We prove existence of L 2-weak solutions of a p-system with boundary conditions. This is done using the vanishing viscosity with mixed Dirichlet-Neumann boundary conditions. Under these boundary conditions the free energy decreases and provides a uniform a priori estimate in L 2 , allowing us to use L 2 Young measures, together with the classical tools of compensated compactness. We then obtain that the viscous solutions converge to weak solutions of the p-system strongly in L p , for any p ∈ [1.2), that satisfy the boundary conditions in the sense given by Definition 2.1. Furthermore the free energy decreases along these solutions.
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Dates et versions

hal-01920905 , version 1 (13-11-2018)
hal-01920905 , version 2 (10-02-2019)
hal-01920905 , version 3 (10-09-2019)

Identifiants

  • HAL Id : hal-01920905 , version 2

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Stefano Marchesani, Stefano Olla. A note on the existence of L^2 valued solutions for a hyperbolic system with boundary conditions. 2018. ⟨hal-01920905v2⟩
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