In this paper,we investigate group-invariant solutions to the hyperbolic geometric flow on Riemann surfaces,which include solutions of separation variables,traveling wave solutions,self-similar solutions and radial so...In this paper,we investigate group-invariant solutions to the hyperbolic geometric flow on Riemann surfaces,which include solutions of separation variables,traveling wave solutions,self-similar solutions and radial solutions.In the proceeding of reduction,there are elliptic,hyperbolic and mixed types of equations.For the first kind of equation,some exact solutions are found;while for the last two kinds,with implicit solutions found,we furthermore investigate whether there will be a global solution or blowing up.Referring to the work of Kong et al.(2009),the results come out perfectly.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
The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we...The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations.Numerical simulations are carried out based on both Reissner-Meissner(R-M)mixed formulations and displacement formulations.Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter c,and reveal that the mechanics of the catenary shells of revolution has some advantages over the spherical shell for some loadings.Two complete codes in Maple are provided.展开更多
In this paper, we prove the existence and uniqueness of global solutions in H^s(R^3) ( s∈R, s≥0) for the initial value problem of the bipolar Schrodinger-Poisson systems.
文摘In this paper,we investigate group-invariant solutions to the hyperbolic geometric flow on Riemann surfaces,which include solutions of separation variables,traveling wave solutions,self-similar solutions and radial solutions.In the proceeding of reduction,there are elliptic,hyperbolic and mixed types of equations.For the first kind of equation,some exact solutions are found;while for the last two kinds,with implicit solutions found,we furthermore investigate whether there will be a global solution or blowing up.Referring to the work of Kong et al.(2009),the results come out perfectly.
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supported by Xi'an University of Architecture and Technology(Grant No.002/2040221134).
文摘The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations.Numerical simulations are carried out based on both Reissner-Meissner(R-M)mixed formulations and displacement formulations.Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter c,and reveal that the mechanics of the catenary shells of revolution has some advantages over the spherical shell for some loadings.Two complete codes in Maple are provided.
文摘In this paper, we prove the existence and uniqueness of global solutions in H^s(R^3) ( s∈R, s≥0) for the initial value problem of the bipolar Schrodinger-Poisson systems.
