We consider a control problem for a thermal convection loop. The problem is governed by a nonline... more We consider a control problem for a thermal convection loop. The problem is governed by a nonlinear partial differential equation with boundary control. We establish the well-posedness of the system, discuss finite element approximations and use a “one mode” approximation to design and compare various control strategies. This system is chaotic and we show that approximate linearization provides an effective
The potential distribution on the scalp produced by current sources in the brain can be measured ... more The potential distribution on the scalp produced by current sources in the brain can be measured by an EEG recorder. The relationship between these sources and the scalp potential distribution may be described by a well-known mathematical model where some simplifications are usually introduced. The head is modeled as a multicompartment nested set and the conductivity of the different tissues is approximated by a positive piecewise constant function. This simplified model is used to solve the forward problem (FP), i.e., to calculate the scalp potential for a current source configuration. In this work, we prove that the weak solutions of the FP are continuous with respect to the conductivity values, that is, the difference between the scalp potentials is small if the conductivity values are closed enough. We present numerical examples that illustrates this property.
We consider a control problem for a thermal convection loop. The problem is governed by a nonline... more We consider a control problem for a thermal convection loop. The problem is governed by a nonlinear partial differential equation with boundary control. We establish the well-posedness of the system, discuss finite element approximations and use a “one mode” approximation to design and compare various control strategies. This system is chaotic and we show that approximate linearization provides an effective
The potential distribution on the scalp produced by current sources in the brain can be measured ... more The potential distribution on the scalp produced by current sources in the brain can be measured by an EEG recorder. The relationship between these sources and the scalp potential distribution may be described by a well-known mathematical model where some simplifications are usually introduced. The head is modeled as a multicompartment nested set and the conductivity of the different tissues is approximated by a positive piecewise constant function. This simplified model is used to solve the forward problem (FP), i.e., to calculate the scalp potential for a current source configuration. In this work, we prove that the weak solutions of the FP are continuous with respect to the conductivity values, that is, the difference between the scalp potentials is small if the conductivity values are closed enough. We present numerical examples that illustrates this property.
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Papers by Diana Rubio