This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and u...This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.展开更多
In the recent past many results have been established on positive solutions to boundary value problems of the form- div (|Du(x)| p-2 Du(x))=λf(u(x))} in} Ω, u(x)=0 on Ω,where λ>0, Ω is a bounded...In the recent past many results have been established on positive solutions to boundary value problems of the form- div (|Du(x)| p-2 Du(x))=λf(u(x))} in} Ω, u(x)=0 on Ω,where λ>0, Ω is a bounded smooth domain and f(s)≥ 0 for s≥ 0 . In this paper we study a priori estimates of positive radial solutions of such problems when N>p>1, Ω=B 1={x∈R N ; | x |<1} and f∈C 1(0,∞)∩ C 0([0,∞)), f(0)=0 .展开更多
We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the ...We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the new a priori estimate for 2D compressible Navier-Stokes equations and a logarithmic estimate for Lamé system.展开更多
This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Cou...This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]： A flow through a duct should be considered as a cal symmetry and should be determined steady, isentropic, irrotational flow with cylindriby solving the 3D potential flow equations with appropriate boundary conditions. By introducing some suitably weighted HSlder spaces and establishing a priori estimates, the authors prove the global existence and stability of a subsonic potential flow in a 3D nozzle when the state of subsonic flow at negative infinity is given.展开更多
Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the we...Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of-Q_(N^u) = Ve^u in bounded domain in R^N, N≥2 are established.Finally, the blow-up behavior of the only singular point is also considered.展开更多
A linear modelling of aeroacoustic waves propagation is discussed. The first point is an existence and uniqueness, theorem. But restrictive assumptions are required on the velocity of the flow. Then a counter example ...A linear modelling of aeroacoustic waves propagation is discussed. The first point is an existence and uniqueness, theorem. But restrictive assumptions are required on the velocity of the flow. Then a counter example proves that they are necessary.展开更多
文摘This paper studies for ward-back ward differential equations with Poisson jumps and with stopping time as termination. Under some weak monotonicity conditions and for non-Lipschitzian coefficients, the existence and uniqueness of solutions are proved via a purely probabilistic approach, while a priori estimate is given. Here, we allow the forward equation to be degenerate.
文摘In the recent past many results have been established on positive solutions to boundary value problems of the form- div (|Du(x)| p-2 Du(x))=λf(u(x))} in} Ω, u(x)=0 on Ω,where λ>0, Ω is a bounded smooth domain and f(s)≥ 0 for s≥ 0 . In this paper we study a priori estimates of positive radial solutions of such problems when N>p>1, Ω=B 1={x∈R N ; | x |<1} and f∈C 1(0,∞)∩ C 0([0,∞)), f(0)=0 .
基金supported by National Natural Science Foundation of China (Grant Nos. 10771097, 10931007)supported by National Natural Science Foundation of China (Grant Nos. 10990013, 11071007)and SRF for ROCS,SEM
文摘We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to 2D compressible Navier-Stokes equations in a bounded domain. The initial vacuum is allowed. The proof is based on the new a priori estimate for 2D compressible Navier-Stokes equations and a logarithmic estimate for Lamé system.
基金supported by the National Basic Research Program of China (No.2006CB805902)the National Natural Science Foundation of China (No.10871096)the Research Foundation for Advanced Talents of Jiangsu University
文摘This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]： A flow through a duct should be considered as a cal symmetry and should be determined steady, isentropic, irrotational flow with cylindriby solving the 3D potential flow equations with appropriate boundary conditions. By introducing some suitably weighted HSlder spaces and establishing a priori estimates, the authors prove the global existence and stability of a subsonic potential flow in a 3D nozzle when the state of subsonic flow at negative infinity is given.
基金Excellent Young Talent Foundation of Anhui Province (Grant No. 2013SQRL080ZD)
文摘Let Q_N be an N-anisotropic Laplacian operator, which contains the ordinary Laplacian operator,N-Laplacian operator and the anisotropic Laplacian operator. We firstly obtain the properties of Q_N, which contain the weak maximal principle, the comparison principle and the mean value property. Then a priori estimates and blow-up analysis for solutions of-Q_(N^u) = Ve^u in bounded domain in R^N, N≥2 are established.Finally, the blow-up behavior of the only singular point is also considered.
文摘A linear modelling of aeroacoustic waves propagation is discussed. The first point is an existence and uniqueness, theorem. But restrictive assumptions are required on the velocity of the flow. Then a counter example proves that they are necessary.
