On Global Large Solutions to 1-D Gas Dynamics

E. E. Endres () and H. K. Jenssen ()
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E. E. Endres: Pennsylvania State University McAllister Building, Department of Mathematics
H. K. Jenssen: Pennsylvania State University McAllister Building, University Park State College, Department of Mathematics

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 593-600 from Springer

Abstract: We consider the 1-D Euler system (1)–(3) describing conservation of mass, momentum, and energy in compressible gas flow. For data with sufficiently small total variation Glimm’s theorem [7] guarantees the existence of a global-in-time weak entropy admissible solution. The solution can be constructed by various methods: the Glimm scheme [7, 10], wave front-tracking [3], semidiscrete schemes [1], or vanishing viscosity [2]. The Euler system plays a distinguished role in the class of general conservation laws and much effort has been invested in extending Glimm's result to larger classes of data. for generic data the solution of the Euler equations is exceedingly complicated with a myriad of interactions resulting in complicated wave patterns.

Keywords: Euler Equation; Shock Speed; Euler System; Transmitted Shock; Wave Strength (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_58

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DOI: 10.1007/978-3-540-75712-2_58

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