作者：
Youjun Xu;Cuie Xiao;Hui Zhu;Hunan City University;Yiyang;...
期刊：
应用数学(英文),2012年3(12):1888-1891 ISSN：2152-7385
作者机构：
Department of Mathematics and Computation Sciences, Hunan City University, Yiyang, China;School of Mathematics and Physics, University of South China, Hengyang, China
关键词：
OPTIMAL;Control;Pontryagin’s;MAXIMUM;PRINCIPLE;STATE;CONSTRAINT;Pontryagin’s Maximum Principle;State Constraint
摘要：
In this paper we investigate optimal control problems governed by a advection-diffusion-reaction equation. We present a method for deriving conditions in the form of Pontryagin’s principle. The main tools used are the Ekeland’s variational principle combined with penalization and spike variation techniques.
摘要：
Abstract: This paper is devoted to a class of inverse coefficient problems for a Parabolic Equation, We obtain an existence and uniqueness theorem of weak solutions. Using the theories of Schauder Fixed-Point Theorem, an existence theorem is established for the inverse coefficient problems solutions.#@#@#摘要: 研究了一类抛物型方程的反系数问题，利用变分方法获得了方程弱解的存在性与唯一性，利用Schauder不动点定理得到了反系数问题解的存在性。
期刊：
Journal of Applied Mathematics and Computing,2010年34(1-2):195-206 ISSN：1598-5865
通讯作者：
Jing, L.(lijingnew@126.com)
作者机构：
[Jing, Li] Department of Mathematics, Changsha University of Science and Technology, Changsha, P.R. China;[Youjun, Xu] School of Mathematics and Physics, University of South China, Hengyang, P.R. China
通讯机构：
[Li Jing] D;Department of Mathematics, Changsha University of Science and Technology, Changsha, P.R. China
关键词：
Existence of quasisolutions;Inverse coefficient problem;Monotonicity;Nonlinear ion transport
摘要：
The problem related to controlled potential experiments in electrochemistry is studied. Ion transport is regarded as the superposition of diffusion and migration. Modelling of the experiment leads to a problem for a nonlinear parabolic equation with additional condition. Driven by the needs of theoretical analysis, from the point of view a inverse coefficient problem, we analyze the monotonicity of input-output mappings in inverse coefficient and source problems for this parabolic equation. Additionally, we extend the nonlinear parabolic equation to a more general case. Under some proper conditions, we investigate the existence of quasisolution of the generalized nonlinear parabolic equation.
期刊：
Journal of Applied Mathematics and Computing,2009年29(1-2):197-206 ISSN：1598-5865
通讯作者：
Xu, Y.(xuyoujun7618@yahoo.com.cn)
作者机构：
[Youjun Xu; Jing Li; Zhenhai Liu] School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410075, China;[Youjun Xu] School of Mathematics and Physics, University of South China, Hengyang, Hunan 421001, China
通讯机构：
[Youjun Xu] S;School of Mathematical Sciences and Computing Technology, Central South University, Changsha, People’s Republic of China<&wdkj&>School of Mathematics and Physics, University of South China, Hengyang, People’s Republic of China
关键词：
Controllability;Parabolic equation;Nonlinear gradient term
摘要：
In this paper, we prove the controllability of a quasi-linear heat equation involving gradient terms with Fourier boundary conditions in a bounded domain ofℝ
N
. The proofs of the main results in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments.
摘要：
In this paper, we consider the existence of insensitizing control for a semilinear heat equation involving gradient terms in unbounded domain Ω. In this case, we prove the existence of controls insensitizing the L2-norm of the observation of the solution in an open subset of the domain. The proofs of the main results in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments.
