| DIFFUSIVE—DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV. COMPRESSIBLE EULER EQUATIONS |
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| 作者姓名： | N. BEDJAOUI P. G. LEFLOCH |
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| 作者单位： | 1. Centre de Mathématiques Appliquées & Centre National de la Recherche Scientifique, UMR 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France;INSSET, Université de Picardie, 48 rue Raspail, 02109 Saint-Quentin, France
2. Centre de Mathématiques Appliquées & Centre National de la Recherche Scientifique, UMR 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France |
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| 摘 要： | 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.
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| 关 键 词： | 可压缩Euler方程 Van－derWaals方程 凸性 行波解 Lax激波不等式 弹性动力学 相变 扩散－分散模型 双曲守恒律 轨迹 |
| 收稿时间： | 4/2/2017 12:00:00 AM |
DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV. COMPRESSIBLE EULER EQUATIONS |
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| N. BEDJAOUI,P. G. LEFLOCH.DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV. COMPRESSIBLE EULER EQUATIONS[J].Chinese Annals of Mathematics,Series B,2003,24(1):17-34. |
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| Authors: | N BEDJAOUI and P G LEFLOCH |
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| Institution: | CentredeMathematiquesAppliquees&CentreNationaldelaRechercheScientifique,UMR7641,EcolePolytechnique,91128PalaiseauCedex,France. |
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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. |
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| Keywords: | Elasto dynamics Phase transitions Hyperbolic conservation law Diffusion Dispersion Shock wave Undercompressive Entropy inequality Kinetic relation |
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