Remarks on non controllability of the heat equation with memory
نویسنده
چکیده
In this paper we deal with the null controllability problem for the heat equation with a memory term by means of boundary controls. For each positive final time T and when the control is acting on the whole boundary, we prove that there exists a set of initial conditions such that the null controllability property fails.
منابع مشابه
Remarks on Null Controllability for Semilinear Heat Equation in Moving Domains
We investigate in this article the null controllability for the semilinear heat operator u − ∆u + f(u) in a domain which boundary is moving with the time t.
متن کاملOn the Null-controllability of the Heat Equation in Unbounded Domains
We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one can not go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the contro...
متن کاملApproximate controllability and lack of controllability to zero of the heat equation with memory
Abstract In this paper we consider the heat equation with memory in a bounded region Ω ⊂ Rd, d ≥ 1, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class C1. We examine its controllability properties both under the action of boundary controls or when the controls are distributed in a subregion of Ω. We prove approximate ...
متن کاملLack of controllability of thermal systems with memory
Heat equations with memory of Gurtin-Pipkin type (i.e. Eq. (1) with α = 0) have controllability properties which strongly resemble those of the wave equation. Instead, recent counterexamples show that when α > 0 the control properties do not parallel those of the (memoryless) heat equation, in the sense that there are initial conditions in L2(Ω) which cannot be controlled to zero. The proof of ...
متن کاملInvestigation of the Effects of Non-Linear and Non-Homogeneous Non-Fourier Heat Conduction Equations on Temperature Distribution in a Semi-Infinite Body
In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011