Controllability and observability of a heat equation with hyperbolic memory kernel
Abbreviated Journal Title
J. Differ. Equ.
Heat equation with memory; Controllability; Observability estimate; Carleman estimate; Highly concentrated approximate solution; INTEGRODIFFERENTIAL EQUATION; SYSTEMS; Mathematics
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. (C) 2009 Elsevier Inc. All rights reserved.
Journal of Differential Equations
"Controllability and observability of a heat equation with hyperbolic memory kernel" (2009). Faculty Bibliography 2000s. 1545.