Boundary controllability of multi-dimensional heat equation with positive control

2015 ◽  
Vol 9 ◽  
pp. 5207-5214
Author(s):  
Mohamed El Azzouzi
Keyword(s):  
Heat Equation ◽  
Positive Control ◽  
Boundary Controllability

scholarly journals Approximate boundary controllability of the heat equation, II

1969 ◽  
Vol 28 (3) ◽  
pp. 482-492 ◽  
Author(s):  
R.C. MacCamy ◽  
V.J. Mizel ◽  
T.I. Seidman
Keyword(s):  
Heat Equation ◽  
Boundary Controllability

A time-optimal boundary controllability problem for the heat equation in a ball

2014 ◽  
Vol 144 (6) ◽  
pp. 1171-1189 ◽  
Author(s):  
Sorin Micu ◽  
Laurenţiu Emanuel Temereancă
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Main Ingredient ◽  
Controllability Problem ◽  
Boundary Controllability ◽  
Müntz Polynomials ◽  
Time Optimal ◽  
Dimensional Ball

The aim of this paper is to study a boundary time-optimal control problem for the heat equation in a two-dimensional ball. The main ingredient is the extension of a result concerning Müntz polynomials due to Borwein and Erdélyi that allows us to prove an observability inequality for the dynamical system's truncation to a finite number of modes. This result, combined with a well-known Lebeau–Robbiano argument used to show the null-controllability of parabolic type equations, enables us to deduce the existence, uniqueness and bang-bang properties for the boundary time-optimal control.

scholarly journals Approximate boundary controllability for the heat equation

1968 ◽  
Vol 23 (3) ◽  
pp. 699-703 ◽  
Author(s):  
R.C MacCamy ◽  
V.J Mizel ◽  
T.I Seidman
Keyword(s):  
Heat Equation ◽  
Boundary Controllability

scholarly journals Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Faker Ben Belgacem ◽  
Sidi Mahmoud Kaber
Keyword(s):  
Heat Equation ◽  
Exact Controllability ◽  
Adjoint Equations ◽  
Boundary Controllability ◽  
The Troubles ◽  
Hilbert Uniqueness Method ◽  
Ill Posed ◽  
Uniqueness Method ◽  
Ill Conditioning

AbstractIll-posedness and/or ill-conditioning are features users have to deal with appropriately in the controllability of diffusion problems for secure and reliable outputs. We investigate those issues in the case of a boundary Dirichlet control, in an attempt to underline the origin of the troubles arising in the numerical computations and to shed some light on the difficulties to obtain good quality simulations. The exact-controllability is severely ill-posed while, in spite of its well-posedness, the null-controllability turns out to be very badly ill-conditioned. Theoretical and numerical results are stated on the heat equation in one dimension to illustrate the specific instabilities of each problem. The main tools used here are first a characterization of the subspace where the HUM (Hilbert Uniqueness Method) control lies and the study of the spectrum of some structured matrices, of Pick and Löwner type, obtained from the Fourier calculations on the state and adjoint equations.

Comparison of localization of metallothionein in tissues of metallothionein-deficient mice

1995 ◽  
Vol 53 ◽  
pp. 1042-1043
Author(s):  
H. Nishimura ◽  
R Nishimura ◽  
D.L. Adelson ◽  
A.E. Michaelska ◽  
K.H.A. Choo ◽  
...  
Keyword(s):  
Metal Binding ◽  
Immunohistochemical Staining ◽  
Squamous Epithelium ◽  
Rabbit Antiserum ◽  
Slight Modification ◽  
Positive Control ◽  
Heavy Metal Binding ◽  
Critical Organ ◽  
Metal Binding Protein ◽  
Deficient Mice

Metallothionein (MT), a cysteine-rich heavy metal binding protein, has several isoforms designated from I to IV. Its major isoforms, I and II, can be induced by heavy metals like cadmium (Cd) and, are present in various organs of man and animals. Rodent testes are a critical organ to Cd and it is still a controversial matter whether MT exists in the testis although it is clear that MT is not induced by Cd in this tissue. MT-IV mRNA was found to localize within tongue squamous epithelium. Whether MT-III is present mainly glial cells or neurons has become a debatable topic. In the present study, we have utilized MT-I and II gene targeted mice and compared MT localization in various tissues from both MT-deficient mice and C57Black/6J mice (C57BL) which were used as an MT-positive control. For MT immunostaining, we have used rabbit antiserum against rat MT-I known to cross-react with mammalian MT-I and II and human MT-III. Immunohistochemical staining was conducted by the method described in the previous paper with a slight modification after the tissues were fixed in HistoChoice and embedded in paraffin.

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