The supersonic flow past a convex combined wedge is discussed. Here the surface of the wedge is composed of two straight lines connected by a convex smooth curve. Under the assumptions that the shock is weak, the ve...The supersonic flow past a convex combined wedge is discussed. Here the surface of the wedge is composed of two straight lines connected by a convex smooth curve. Under the assumptions that the shock is weak, the vertex of the wedge is less than a critical value and the difference of the slope of these two lines is small, the author proves the global existence of solution with shock front and obtains the asymptotic bebaviour of the solution.展开更多
Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appro...Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals.展开更多
This paper considers a class of fourth order nonlinear difference equations Δ<sup>2</sup>（r<sub>n</sub>Δ<sup>2</sup>y<sub>n</sub>）+ f（n,y<sub>n</sub>）=...This paper considers a class of fourth order nonlinear difference equations Δ<sup>2</sup>（r<sub>n</sub>Δ<sup>2</sup>y<sub>n</sub>）+ f（n,y<sub>n</sub>）=0,n∈N（n<sub>0</sub>）,where f（n,y）may be classified as superlinear,sublinear,strongly super- linear and strongly sublinear.In superlinear and sublinear cases,necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.In strongly superlinear and strongly sublinear cases,sufficient conditions are given for all solutions to be oscillatory.展开更多
The stability of the weak planar oblique shock front with respect to the perturbation of the wall is discussed. By the analysis of the formation and the global construction of shock and its asymptotic behaviour for st...The stability of the weak planar oblique shock front with respect to the perturbation of the wall is discussed. By the analysis of the formation and the global construction of shock and its asymptotic behaviour for stationary supersonic flow along a smooth rigid wall we obtain the stability of the solution containing a weak planar shock front. The stability can be used to single out a physically reasonable solution together with the entropy condition.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
文摘The supersonic flow past a convex combined wedge is discussed. Here the surface of the wedge is composed of two straight lines connected by a convex smooth curve. Under the assumptions that the shock is weak, the vertex of the wedge is less than a critical value and the difference of the slope of these two lines is small, the author proves the global existence of solution with shock front and obtains the asymptotic bebaviour of the solution.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19701018)
文摘Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals.
基金Partially Supported by the National Science Foundation of China
文摘This paper considers a class of fourth order nonlinear difference equations Δ<sup>2</sup>（r<sub>n</sub>Δ<sup>2</sup>y<sub>n</sub>）+ f（n,y<sub>n</sub>）=0,n∈N（n<sub>0</sub>）,where f（n,y）may be classified as superlinear,sublinear,strongly super- linear and strongly sublinear.In superlinear and sublinear cases,necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties.In strongly superlinear and strongly sublinear cases,sufficient conditions are given for all solutions to be oscillatory.
基金This work was partially supported by Key Grant of NMST of China the National Natural Science Foundation of China the Doctoral Programme Foundation of NEM.
文摘The stability of the weak planar oblique shock front with respect to the perturbation of the wall is discussed. By the analysis of the formation and the global construction of shock and its asymptotic behaviour for stationary supersonic flow along a smooth rigid wall we obtain the stability of the solution containing a weak planar shock front. The stability can be used to single out a physically reasonable solution together with the entropy condition.
基金supported by an NSERC granta startup fund of University of Alberta
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
