Title

Controllability And Observability Of A Heat Equation With Hyperbolic Memory Kernel

Keywords

Carleman estimate; Controllability; Heat equation with memory; Highly concentrated approximate solution; Observability estimate

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. © 2009 Elsevier Inc. All rights reserved.

Publication Date

10-15-2009

Publication Title

Journal of Differential Equations

Volume

247

Issue

8

Number of Pages

2395-2439

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jde.2009.07.026

Socpus ID

68949099432 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/68949099432

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