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研究生:周曉芳
研究生(外文):Hsiao-Fang Chou
論文名稱:一個四階半線性拋物型方程的零邊界控制
論文名稱(外文):Null Boundary Controllability for A Fourth Order Semilinear Parabolic Equation
指導教授:林月珍
指導教授(外文):Yung-Jen Lin Guo
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:29
中文關鍵詞:邊界控制半線性拋物
外文關鍵詞:Boundary controlSemilinearParabolic
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We consider the null boundary controllability for a one-dimensional fourth order semilinear parabolic equation. We show that if the initial data is continuous and sufficiently small, then the fourth order semilinear parabolic equation is controllable.

We consider the null boundary controllability for a one-dimensional fourth order semilinear parabolic equation. We show that if the initial data is continuous and sufficiently small, then the fourth order semilinear parabolic equation is controllable.

1. Introduction
2. Solutions of the Cauchy Problem in the x-Direction
3. Existence of Boundary Controllers
References

1. H. O. Fattorni, Boundary control systems, SIAM J. Control 6 (1968), 349-388.
2. H. O. Fattorni and D. L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Rational. Mech. Anal. 43 (1971), 272-292.
3. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
4. Y. -J. L. Guo, Exact boundary controllability for heat equation with time dependent coefficients, Taiwanness J. Math. 4 (2000), 307-320.
5. Y. -J. L. Guo, Null boundary controllability for a fourth order parabolic equation, Taiwanness J. Math., (2002) (in press).
6. Y. -J. L. Guo and W. Littman, Null boundary controllability for semilinear heat equations, Appl. Math. Optim. 32(3) (1995), 281-316.
7. L. Hormander, Linear Partial Differential Operators, Academic Press, New York, 1963.
8. D. Kinderlehrer and L. Nirenberg, Analytic at the boundary of solutions of nonlinear second-order parabolic equations, Comm. Pure. and Applied Math. 31 (1978), 283-338.
9. O. A. Ladyzenskaja, V. A. Solonnokov and N. N. Uraceva, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, RI, 1968.
10. P. -L. Lee and Y. -J. L. Guo, Gevrey class regularity for parabolic equations, Differential and Integral Equations, 14
(2001), 989-1004.
11. L. Mora, Semilinear parabolic problems define demiflows on C^k spaces, Trans. Amer. Math. Soc. 278(10 (1983), 21-55.
12. L. Nirenberg, Uniqueness in Cauchy problems for differential equations with constant leading coefficients, Comml Pure Appl. Math. 10 (1957), 89-105.

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