半轴上变系数热方程的可控性问题

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-05-10 DOI:10.1051/cocv/2022041

L. Fardigola, K. Khalina

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引用次数: 0

摘要

本文研究了由Dirichlet边界条件控制的热方程$w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$, $x>0$, $t\in(0,T)$的可控性和近似可控性问题。控制在$L^\infty(0,T)$中被考虑。证明了该系统的每一个初始状态对其在给定时间内的任何最终状态都是近似可控的$T>0$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Controllability problems for the heat equation with variable coefficients on a half-axis

In the paper, the problems of controllability and approximate controllability are studied for the heat equation $w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$ , $x>0$ , $t\in(0,T)$ , controlled by the Dirichlet boundary condition. Control is considered in $L^\infty(0,T)$ . It is proved that each initial state of this system is approximately controllable to any its end state in a given time $T>0$ .

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Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

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期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.