Controllability and observability of a heat equation with hyperbolic memory kernel

By Xiaoyu Fu, Jiongmin Yong, Xu Zhang. 2009

62 citations recorded by the source corpus.

Abstract The exact controllability and observability for a heat equation with hyperbolic memory kernel in anisotropic and nonhomogeneous media are considered. Due to the appearance of such a kind of memory, the speed of propagation for solutions to the heat equation is finite and the corresponding controllability property has a certain nature similar to hyperbolic equations, and is significantly different from that of the usual parabolic equations. By means of Carleman estimate, we establish a positive controllability and observability result under some geometric condition. On the other hand, by a careful construction of highly concentrated approximate solutions to hyperbolic equations with memory, we present a negative controllability and observability result when the geometric condition is not satisfied.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8feb5a2247ca487fd380fe7b4a80e4dbec24b7ea

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Null Controllability for Wave Equations with Memory (2015, background): “In the literature, the controllability problems for evolution equations with memory terms have been studied extensively (See [2, 15, 17, 21, 22, 25, 26, 28, 32, 33, 35] and the references therein).”