Minimal time control problem of a linear heat equation with memory

2021 ◽  
Vol 157 ◽  
pp. 105052
Author(s):  
Lijuan Wang ◽  
Xiuxiang Zhou
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
Minimal Time ◽  
Time Control ◽  
Heat Equation With Memory ◽  
With Memory

scholarly journals Insensitizing control for linear and semi-linear heat equations with partially unknown domain

2019 ◽  
Vol 25 ◽  
pp. 50 ◽  
Author(s):  
Pierre Lissy ◽  
Yannick Privat ◽  
Yacouba Simporé
Keyword(s):  
Heat Equation ◽  
Control Problem ◽  
Duality Theory ◽  
Unique Continuation ◽  
Dirichlet Boundary Conditions ◽  
Linear Case ◽  
Heat Equations ◽  
Geometrical Approach ◽  
Linear Heat Equation ◽  
Linear Heat

We consider a semi-linear heat equation with Dirichlet boundary conditions and globally Lipschitz nonlinearity, posed on a bounded domain of ℝN (N ∈ ℕ*), assumed to be an unknown perturbation of a reference domain. We are interested in an insensitizing control problem, which consists in finding a distributed control such that some functional of the state is insensitive at the first order to the perturbations of the domain. Our first result consists of an approximate insensitization property on the semi-linear heat equation. It rests upon a linearization procedure together with the use of an appropriate fixed point theorem. For the linear case, an appropriate duality theory is developed, so that the problem can be seen as a consequence of well-known unique continuation theorems. Our second result is specific to the linear case. We show a property of exact insensitization for some families of deformation given by one or two parameters. Due to the nonlinearity of the intrinsic control problem, no duality theory is available, so that our proof relies on a geometrical approach and direct computations.

scholarly journals An optimal time control problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter

2017 ◽  
Vol 51 (4) ◽  
pp. 1289-1299 ◽  
Author(s):  
Karim Benalia ◽  
Claire David ◽  
Brahim Oukacha
Keyword(s):  
Heat Equation ◽  
Optimal Time ◽  
One Dimensional ◽  
Scaling Parameter ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
Time Control ◽  
Time Problem ◽  
Type Property ◽  
The One

In this paper, we study the optimal time problem for the one-dimensional, linear heat equation, in the presence of a scaling parameter. To begin with, we build an exact solution. The dependence of this solution as regards the scaling parameter naturally opens the way to study the existence and uniqueness of an optimal time control. If, moreover, one assumes the L∞ − null controllability, it enables to establish a bang-bang type property.

Dynamic behavior of a heat equation with memory

2009 ◽  
Vol 32 (10) ◽  
pp. 1287-1310 ◽  
Author(s):  
Jun-Min Wang ◽  
Bao-Zhu Guo ◽  
Meng-Yin Fu
Keyword(s):  
Heat Equation ◽  
Dynamic Behavior ◽  
Heat Equation With Memory ◽  
With Memory
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