Bi-objective and hierarchical control for the Burgers equation

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-03-15 DOI:10.1007/s00028-024-00952-z

F. D. Araruna, E. Fernández-Cara, L. C. da Silva

引用次数: 0

Abstract

We present some results concerning the control of the Burgers equation. We analyze a bi-objective optimal control problem and then the hierarchical null controllability through a Stackelberg–Nash strategy, with one leader and two followers. The results may be viewed as an extension to this nonlinear setting of a previous analysis performed for linear and semilinear heat equations. They can also be regarded as a first step in the solution of control problems of this kind for the Navier–Stokes equations.

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布尔格斯方程的双目标和分层控制

我们介绍了有关布尔格斯方程控制的一些结果。我们分析了一个双目标最优控制问题，然后通过一个领导者和两个跟随者的 Stackelberg-Nash 策略分析了分层空可控性。这些结果可以看作是之前对线性和半线性热方程分析在非线性环境下的扩展。这些结果也可视为解决 Navier-Stokes 方程中此类控制问题的第一步。

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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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators