| Solvability of the nonlinear Airy equation on a torus |
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| 作者姓名： | 张兴友 |
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| 作者单位： | College of |
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| 基金项目： | the Scientific Research Foundation for Returned Overseas Chinese Scholars under the State Education Ministry，and the Young Key Teachers?Foundation of Chongqing University. |
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| 摘 要： | 1. Introduction Consider the problem (P) below 2 i(), for (,),txxxuuuuufxxtT++++=未a where the initial condition is 0(0,)()uxux=. Herein 0u and 2()fLT are square integrable complex functions on T; T is the 1-dimensional torus, +Ris the set of positive numbers, and a a real positive number. This type of equation was first introduced in the study of optical fibers 1]. Y. Martel 2] proved the well-posedness for the case of whole space R(the set of all real numbers) with a = …
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| 关 键 词： | nonlinear evolution equations Airy equation Bourgain抯 spaces |
Solvability of the nonlinear Airy equation on a torus |
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| ZHANG Xingyou,TANG Yan College of Mathematics and Sciences,Chongqing University,Chongqing,P.R. China.Solvability of the nonlinear Airy equation on a torus[J].Journal of Chongqing University,2003,2(1). |
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| Authors: | ZHANG Xingyou TANG Yan College of Mathematics and Sciences Chongqing University Chongqing PR China |
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| Institution: | College of Mathematics and Sciences, Chongqing University, Chongqing 400044, P.R. China |
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| Abstract: | The solvability of the nonlinear Airy equation on a torus is studied, With the help of Bourgain's 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. |
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| Keywords: | nonlinear evolution equations Airy equation Bourgain's spaces |
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