**Îµ-Insensitizing
Controls for the Heat Equation**
**Luz de Teresa**

deteresa@matem.unam.mx

*Instituto de Matemáticas, UNAM*

Circuito Exterior, C.U.

Mexico, D.F., Mexico

**Abstract:**
We consider a heat equation with partially known initial data. We define
a functional on the solutions (the square LÂ² norm on an
observation set) of the heat equation and acting with a control with
support in an open subset of the domain try to obtain that the derivative
of the functional , with respect to a small parameter of the perturbed
initial data, is small. This problem is called the Îµ-insensitizing
problem for the heat equation and can easily be transformed in an approximate
control problem for a cascade system of heat equations. This problem
can be transformed in a unique continuation problem for the adjoint
of the cascade system that has a particular interest when the control
and observation regions have empty intersection.

**A
Numerical Conjugate Gradient Method for ytt - yxx + y3 = 0**
**Carlos Barrón Romero**

cbarron@correo.cua.uam.mx

UAM Unidad Cuajimalpa

División de Ciencias Naturales e Ingeniería

Departamento de Matemáticas Aplicadas y Sistemas

México, D. F., Mexico

**Abstract:**
A Conjugate Gradient Control Method will be depicted and will present
numerical results for the problem in the title, following the variational
techniques of Glowinski and Lions.

**Conjugate
Gradient Methods for the Estimation of Hydrodynamic Vector Fields **
**L. Hector Juarez**

hect@xanum.uam.mx

**Marco A. Nunez**

manp@xanum.uam.mx

**Ciro F. Flores**

ciro.flores@itesm.mx

**Abstract: **Diagnostic
models in meteorology generate a wind field satisfying some time-independent
physical constraints. Among these models, mass--consistent models play
an important role, [1]. We study a variational method based on Sasaki's
method [2], which provide an adjusted field by the minimization of a
functional with a mass conservation constraint. Based on previous experience
about the solution of Stokes-like problems in CFD [3], we introduce
a methodology based on iterative conjugate gradient methods with preconditioning
to solve the primitive problem (a minimization problem with a constraint).

**Matrix
Calculation of Perturbation Series for Self-Adjoint Operators**

Marco A. Nuñez

manp@xanum.uam.mx
**Gustavo Izquierdo B.**

iubg@xanum.uam.mx

*Departamento de Fisica*

Universidad Autonoma Metropolitana Iztapalapa

Distrito Federal, Mexico

**Abstract:**
A matrix approach to compute the perturbation series of perturbed self-adjoint
operators is proposed. It is shown that the series can be computed by
means of those corresponding to a matrix representation, when the zeroth
order operator is perturbed by an operator relatively bounded by the
former. This result includes Schroedinger operators of atomic and molecular
systems, confined spatially in a box with impenetrable walls. The results
are extended to zeroth order operators, for which the standard Rayleigh-Schroedinger
perturbation theory does not work. In this case we have Schroedinger
operators with a finite number of bounded states. The approach allows
the calculation of perturbation series even when the eigenstates of
the zeroth order operator are unknown. Numerical examples are given.
A heuristic argument suggests that the approach can be applied to compute
the perturbation series of singularly perturbed operators and numerical
examples that support such a conjecture are given.