Displaying similar documents to “Kinetic Approach to Systems of Conservation Laws”

Convergence of Vanishing Viscosity Approximations of 2 x 2 Triangular Systems of Multi-Dimensional Conservation Laws

G. M. Coclite, K. H. Karlsen, S. Mishra, N. H. Risebro (2009)

Bollettino dell'Unione Matematica Italiana

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We consider a multidimensional triangular system of conservation laws. These equations arise in models of three phase flows in porous media and include multi dimensional conservation laws with discontinuous coefficients as special cases. We study approximate solutions of these equations constructed by the vanishing viscosity method and show that the approximate solutions converge to a weak solution of the multi-dimensional triangular system.

Laws of nature, exceptions and tropes

Max Kistler (2003)

Philosophia Scientiae

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I propose a realist theory of laws formulated in terms of tropes (or property instances) that avoids both the problems of the “best-systems-analysis” and the “inference problem” of realism of universals. I analyze the concept of an exceptional situation, characterized as a situation in which a particular object satisfies the antecedent but not the consequent of the regularity associated with a law, without thereby falsifying that law. To take this possibility into account, the properties...

The Boltzmann Equation: Mathematics and Applications

Carlo Cercignani (2007)

Bollettino dell'Unione Matematica Italiana

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The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning...