This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to th...This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.展开更多
This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness ...This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness and existence of solutions are proved by a new method.展开更多
In this paper, the Tricomi problem for the nonlinear equation of a mixed type k（x,y）u<sub>xx</sub>+u<sub>yy</sub>+α（x,y）u<sub>x</sub>+β（x,y）u<sub>y</sub>+γ（x,y...In this paper, the Tricomi problem for the nonlinear equation of a mixed type k（x,y）u<sub>xx</sub>+u<sub>yy</sub>+α（x,y）u<sub>x</sub>+β（x,y）u<sub>y</sub>+γ（x,y）u-|u|<sup>ρ</sup>u = f（x,y）is considered. Under very weak conditions, the existence. of H<sup>1</sup> strong solution is proved byapplying the energy integral and the fixed point principle.展开更多
In this paper,the Tricomi problem and the generalized Tricomi problem for a quasilinear mixed type equation are studied.The coefficients of the mixed type equation are discontinuous on the line,where the equation chan...In this paper,the Tricomi problem and the generalized Tricomi problem for a quasilinear mixed type equation are studied.The coefficients of the mixed type equation are discontinuous on the line,where the equation changes its type.The existence of solution to these problems is proved.The method developed in this paper can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.展开更多
In this paper, the L, weak solution and H^1 strong solution to the Tricomi problem of in-finitesimal deformation equation for surfaces witb a mixed curvatute are proved under veryweak conditions.
In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of soluti...In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.展开更多
The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and t...The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.展开更多
In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {（t,x）：t∈[1,＋∞）,x∈Rn} with the initial data given on the line t=1 in...In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {（t,x）：t∈[1,＋∞）,x∈Rn} with the initial data given on the line t=1 in Hadamard＇s sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate.展开更多
基金partially supported by National Natural Science Foundation of China (10531020)the National Basic Research Program of China (2006CB805902)+1 种基金the Project STCSM(06JC14005)the Doctorial Foundation of National Educational Ministry (20050246001)
文摘This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.
基金This research is supported by NSFC (No. 10471149)
文摘This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness and existence of solutions are proved by a new method.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, the Tricomi problem for the nonlinear equation of a mixed type k（x,y）u<sub>xx</sub>+u<sub>yy</sub>+α（x,y）u<sub>x</sub>+β（x,y）u<sub>y</sub>+γ（x,y）u-|u|<sup>ρ</sup>u = f（x,y）is considered. Under very weak conditions, the existence. of H<sup>1</sup> strong solution is proved byapplying the energy integral and the fixed point principle.
基金Project supported by the National Natural Science Foundation of China (No.10531020)the National Basic Research Program of China (No.2006CB805902)+1 种基金the Doctorial Program Foundation of the Ministry of Education of Chinathe Science and Technology Commission of Shanghai Municipality
文摘In this paper,the Tricomi problem and the generalized Tricomi problem for a quasilinear mixed type equation are studied.The coefficients of the mixed type equation are discontinuous on the line,where the equation changes its type.The existence of solution to these problems is proved.The method developed in this paper can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, the L, weak solution and H^1 strong solution to the Tricomi problem of in-finitesimal deformation equation for surfaces witb a mixed curvatute are proved under veryweak conditions.
基金Supported by NNSF of China(Tianyuan Fund of Mathematics11326152)+1 种基金NSF of Jiangsu Province of China(BK20130736)the Research Fund of Nanjing Institute of Technology of China(YKJ201339)
基金supported by National Natural Science Foundation of China (10531020)the Doctorial Foundation of National Educational Ministry (20090071110002)
文摘In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.
文摘The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.
基金Supported by National Natural Science Foundation of China (Grant No.11001122)Scientific Research Fund of Nanjing Institute of Technology (Grant No.YKJ201113)
文摘In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {（t,x）：t∈[1,＋∞）,x∈Rn} with the initial data given on the line t=1 in Hadamard＇s sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate.
