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| DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV. COMPRESSIBLE EULER EQUATIONS |
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Citation： |
N. BEDJAOUI,P. G. LEFLOCH.DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV. COMPRESSIBLE EULER EQUATIONS[J].Chinese Annals of Mathematics B,2003,24(1):17~34 |
| Page view： 1301
Net amount： 865 |
Authors： |
N. BEDJAOUI; P. G. LEFLOCH |
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| Abstract： |
The authors consider the Euler equations for a compressible fluid in one space dimension
when the equation of state of the fluid does not fulfill standard convexity assumptions and
viscosity and capillarity effects are taken into account. A typical example of nonconvex constitutive
equation for fluids is Van der Waals’ equation. The first order terms of these partial
differential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class of
nonconvex equations of state, an existence theorem of traveling waves solutions with arbitrary
large amplitude is established here. The authors distinguish between classical (compressive) and
nonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequalities,
and are characterized by the so-called kinetic relation, whose properties are investigated
in this paper. |
Keywords： |
Elastodynamics, Phase transitions, Hyperbolic conservation law, Diffusion,
Dispersion, Shock wave, Undercompressive, Entropy inequality, Kinetic relation |
Classification： |
35L65, 35M20, 74J40, 76N |
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