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SPATIALLY PERIODIC SOLUTIONS FOR GAS FLOWS WITH PRESSURE DEPENDING ON A VARIABLE COEFFICIENT

FRID, HERMANO ; RISEBRO, NILS HENRIK ; SANDE, HILDE

Journal of hyperbolic differential equations, 2013-03, Vol.10 (1), p.129-148 [Periódico revisado por pares]

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Título:
SPATIALLY PERIODIC SOLUTIONS FOR GAS FLOWS WITH PRESSURE DEPENDING ON A VARIABLE COEFFICIENT
Autor: FRID, HERMANO ; RISEBRO, NILS HENRIK ; SANDE, HILDE
Assuntos: Coefficients ; Decay ; Density ; Entropy ; Gas flow ; Inequalities ; Mathematical models ; Smoothness ; Specific volume
É parte de: Journal of hyperbolic differential equations, 2013-03, Vol.10 (1), p.129-148
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: We study the global existence of spatially periodic solutions for certain models of gas flow in Lagrangian coordinates for which the pressure has the form $p(\mathcal{E}, v) = \kappa(\mathcal{E})v^{-\gamma(\mathcal{E})}$ , where v, as usual, is the specific volume, and $\kappa(\mathcal{E})>0$ , $\gamma(\mathcal{E}) > 1$ are smooth functions of the variable coefficient $\mathcal{E} = \mathcal{E}(x, t)$ , which is assumed to satisfy suitable smoothness and decay properties, in particular, $\mathcal{E}(x, t) \to \bar{\mathcal{E}}$ , uniformly, as t →0. One important feature of our analysis is that the initial total variation over one period may be taken as large as we wish as long as $\gamma(\bar{\mathcal{E}})$ is sufficiently close to 1. We also prove a non-homogeneous entropy inequality which implies the decay of the solution to the mean value as t → ∞.
Editor: Singapore: World Scientific Publishing Company
Idioma: Inglês

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