By D. Aregba-Driollet, R. Natalini (auth.), Michael Fey, Rolf Jeltsch (eds.)

ISBN-10: 3034887205

ISBN-13: 9783034887205

ISBN-10: 3034897421

ISBN-13: 9783034897426

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Extra info for Hyperbolic Problems: Theory, Numerics, Applications: Seventh International Conference in Zürich, February 1998 Volume I

Sample text

Moreover, taking into account dissipative terms, these laws become where we have set s p pk = p'Y' St = p5/3' SE = pE p2Cl/3+l' Travelling Wave Solutions of the (k, E) System 51 The properties i) and ii) can be found in [1], [4] and [5]. The property iii) completes the previous results concerning Lax: entropy pairs and their compatibility with dissipative phenomena. Three particular cases are of interest: p p b -1) 2 atP- + axp-u = -(-1-) J-L(axu) > 0, p'Y p'Y P "1pk pk 1 2 atP p5/3 + axp p5/3 u = p2/3 J-Lt(axu) > 0 (11) (12) and E atP kGl E + axp kGl u = O.

Fr International Series of Numerical Mathematics Vol. 129, © 1999 Birkhiiuser Verlag Basel/Switzerland Travelling Wave Solutions of a Convective Diffusive System with First and Second Order Terms in Nonconservation Form Christophe Berthon and Frederic Coquel Abstract. The present work is devoted to the study of travelling wave solutions of a convective dissipative system, the so-called (k, E) system modelling turbulent compressible flows. This system exhibits non conservative products for both the first order and second order operators.

42 (1989), 815-844. [6] C. M. Dafermos, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Differential Equations, 14 (1973), 202-212. [7] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. , 18 (1965), 697-715. [8] J. Glimm - P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws, Amer. Math. Soc. Memoir, No. 101. S. Providence, 1970. [9] H. Hattori, The Riemann problem for a van der Waals fluid with entropy rate admissible criterion - Isothermal Case, Arch.

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Hyperbolic Problems: Theory, Numerics, Applications: Seventh International Conference in Zürich, February 1998 Volume I by D. Aregba-Driollet, R. Natalini (auth.), Michael Fey, Rolf Jeltsch (eds.)


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