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
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
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 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.
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.
