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 existenc...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.展开更多
Motivated by [3], [4] and [5], we present the kinetic formulation of a nonlinear variational wave equation corresponding to some specific weak solutions . This equation arises from studies in nematic liquid crystals, ...Motivated by [3], [4] and [5], we present the kinetic formulation of a nonlinear variational wave equation corresponding to some specific weak solutions . This equation arises from studies in nematic liquid crystals, long wave on a dipole chain and a few other fields.展开更多
The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation a...The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.展开更多
基金Sponsored by the Foundation of Yancheng Teachers University (07YCKL061)
文摘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.
文摘Motivated by [3], [4] and [5], we present the kinetic formulation of a nonlinear variational wave equation corresponding to some specific weak solutions . This equation arises from studies in nematic liquid crystals, long wave on a dipole chain and a few other fields.
基金supported by the National Natural Science Foundation of China (No. 10971135)the Program for New Century Excellent Talents of the Ministry of Education of China (No. NCET-07-0546)+2 种基金the University Young Teacher Sciences Foundation of Anhui Province (No. 2010SQRL145)Shanghai Jiao Tong University Innovation Fund for Postgraduates (No. AE071202)the Quality Project Fund of Fuyang Teachers College (No. 2010JPKC07)
文摘The authors are concerned with a zero-flux type initial boundary value problem for scalar conservation laws.Firstly,a kinetic formulation of entropy solutions is established.Secondly,by using the kinetic formulation and kinetic techniques,the uniqueness of entropy solutions is obtained.Finally,the parabolic approximation is studied and an error estimate of order η 1/3 between the entropy solution and the viscous approximate solutions is established by using kinetic techniques,where η is the size of artificial viscosity.
