Displaying similar documents to “High order approximation of probabilistic shock profiles in hyperbolic conservation laws with uncertain initial data”

The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section

Dietmar Kröner, Philippe G. LeFloch, Mai-Duc Thanh (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [ (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a...

The entropy principle: from continuum mechanics to hyperbolic systems of balance laws

Tommaso Ruggeri (2005)

Bollettino dell'Unione Matematica Italiana

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We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for...

A new approach to mutual information

Fumio Hiai, Dénes Petz (2007)

Banach Center Publications

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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.