| Swift-Hohenberg方程的打靶法 |
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| 引用本文： | 陶友山,张寄洲. Swift-Hohenberg方程的打靶法[J]. 高校应用数学学报(英文版), 2002, 17(4): 391-403. DOI: 10.1007/s11766-996-0003-6 |
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| 作者姓名： | 陶友山 张寄洲 |
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| 作者单位： | Tao Youshan Zhang JizhouDept.of Appl.Math.，Donghua Univ.，Shanghai 200051，China.College of Math. Sci.，Shanghai Normal Univ.，Shanghai 200234，China. |
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| 基金项目： | National Natural Science Foundation of China (1 0 0 71 0 67) |
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| 摘 要： | § 1 IntroductionIn this paper we shall study the formation of spatially periodic patterns in extendedsystems described by Swift- Hohenberg equationut=ku - 1 +2x22 u - u3 ,k∈ R. (1.1)This equation was first proposed in 1976 by Swiftand Hohenberg[12 ] as a simple model forthe Rayleigh- B nard instability of roll waves.However,since then an effective m odel e-quation has been proved for a variety of system s in physics and mechanics.The Swift- Hohenberg equation has been studied a …
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| 关 键 词： | SWIFT-HOHENBERG方程 打靶法 相变点 周期解 |
| 收稿时间： | 2002-02-19 |
A shooting method for the Swift-Hohenberg equation |
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| Youshan Tao,Jizhou Zhang. A shooting method for the Swift-Hohenberg equation[J]. Applied Mathematics A Journal of Chinese Universities, 2002, 17(4): 391-403. DOI: 10.1007/s11766-996-0003-6 |
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| Authors: | Youshan Tao Jizhou Zhang |
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| Affiliation: | (1) Dept. of Appl. Math., Donghua Univ., 200051 Shanghai, China;(2) College of Math. Sci., Shanghai Normal Univ, 200234 Shanghai, China |
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| Abstract: | Stationary even single-bump periodic solutions of the Swift-Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1, there exist periodic solutions having the same energy as the constant solution u=0; if 1<k<3/2, there exist periodic solutions having the same energy as the stable states u=±√k−1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument. Partially supported by the National Natural Science Foundation of China (10071067). |
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| Keywords: | shooting technique Swift Hohenberg equation critical point periodic solution. |
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