Acta mathematica scientia, Series B >
THE APPLICATION OF THE KINETIC FORMULATION TO A SYSTEM OF QUADRATIC FLUX
Received date: 2006-12-13
Revised date: 2007-09-03
Online published: 2009-09-20
Supported by
Sponsored by the Foundation of Yancheng Teachers University (07YCKL061)
In this article, the author uses the compensated compactness method coupled with some basic ideas of the kinetic formulation developed by Lions, Perthame, Souganidis and Tadmor to give a refined proof for the
existence of global entropy solutions to a system of quadratic flux. The fire-new method of reduction of Young measures is a pith of this work.
Key words： strong entropy; entropy solution; kinetic formulation
CHENG Zhi-Xin . THE APPLICATION OF THE KINETIC FORMULATION TO A SYSTEM OF QUADRATIC FLUX[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1375 -1382 . DOI: 10.1016/S0252-9602(09)60110-7
[1] Lu Y G. Convergence of the viscosity method for a nonstrictly hyperbolic system. Acta Math Sci, 1992, 12: 230--239
[2] Kan P T. On the Cauchy problem of a 2×2 system of nonstrictly hyperbolic conservation laws
[D]. New York Univ, 1989
[3] Lu Y G. Hyperbolic Conservation Laws and the Compensated Compactness Method. 128, Chapman and Hall. New York: CRC Press, 2002
[4] James F J, Peng Y J, Perthame B. Kinetic formulation for chromatography and some other hyperbolic systems.
J Math Pure Appl, 1995, 74: 367--385
[5] Lu Y G. Existence of global entropy solutions to a nonstrictly hyperbolic system. Arch Rational Mech Anal, 2005, 178: 287--299
[6] Lions P L, Perthame B, Souganidis P E. Existence and stability of entropy solutions for the hyperbolic
systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Comm Pure Appl Math, 1996, 49: 599--638
[7] Lions P L, Perthame B, Tadmor E. Kinetic formulation of the isentropic gas dynamics and p-system.
Commun Math Phys, 1994, 163: 415--431
[8] Murat F. Compacitépar compensation. Ann Scuola Norm Sup Pisa, 1978, 5: 489--507
[9] Tartar T. Compensated compactness and applications to partial differential equations//Knops R J, ed.
Research Notes in Mathematocs, Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, 4. London: Pitman Press, 1979
[10] Chen G Q, Kan P T. Hyperbolic conservation laws with umbilic degeneracy I. Arch Rat Mech Anal, 1995, 130: 231--276
/
| 〈 |
|
〉 |