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The Research Summary of the Controllability of Semilinear Heat Equation
Author: SunNa
Tutor: GaoHang
School: Northeast Normal University
Course: Operational Research and Cybernetics
Keywords: approximate controllablility exact controllability monotone operator globally Lipschitz
CLC: O175
Type: Master's thesis
Year: 2007
Downloads: 50
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Abstract
Heat equations is a kind of fundamental equations in the controllability of PDES.In recent years,the control problems of the semilinear heat equations has received a great deal of attention from mathematicians.In this article we have done some research summary into the controllalility for semilinear heat equations. First,we introduce the controllability for the linear heat equations in bouded domains of R. Then,we consider the approximate controllability for the semilinear heat equation. Approximate controllability for the semilinear heat equation is got by this way that linearing the system by variational approach and constructing functional and using dual equation. At last, using the BrowderMinty theorem from the theory of monotone operators,we consider the exact internal controllability for the semilinear heat equation.We show that the system is exactly controllable in L~2(Ω) if the nonlinearities are globally Lipschitz continuous.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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