The solvability of the nonlinear Airy equation on a torus is studied. With the help of Bourgain抯 spaces, the existence of a global in time solution to a forced damped nonlinear Airy equation on the 1-dimensional toru...The solvability of the nonlinear Airy equation on a torus is studied. With the help of Bourgain抯 spaces, the existence of a global in time solution to a forced damped nonlinear Airy equation on the 1-dimensional torus is proved by deriving it from that of the local solution.展开更多
This paper is concerned with the second order linear differential equationd 2ydx 2-x λ y=0, which is called the generalized Airy equation of order λ , where the constant λ≥ 0 (not necessary pos...This paper is concerned with the second order linear differential equationd 2ydx 2-x λ y=0, which is called the generalized Airy equation of order λ , where the constant λ≥ 0 (not necessary positive integer) satisfies (-1) λ =± 1 . The properties of its two special linearly independent real-valued solutions, called the generalized Airy function of order λ , are systematically investigated.展开更多
基金the Scientific Research Foundation for Returned Overseas Chinese Scholars under the State Education Ministrythe Young Key Teachers' Foundation of Chongqing University.
文摘The solvability of the nonlinear Airy equation on a torus is studied. With the help of Bourgain抯 spaces, the existence of a global in time solution to a forced damped nonlinear Airy equation on the 1-dimensional torus is proved by deriving it from that of the local solution.
文摘This paper is concerned with the second order linear differential equationd 2ydx 2-x λ y=0, which is called the generalized Airy equation of order λ , where the constant λ≥ 0 (not necessary positive integer) satisfies (-1) λ =± 1 . The properties of its two special linearly independent real-valued solutions, called the generalized Airy function of order λ , are systematically investigated.
