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This article addresses the problem of distributed-parameter control for a class of infinite-dimensional manufacturing processes with scanned thermal actuation, such as scan welding. This new process is implemented on a robotic GTAW laboratory setup with infrared pyrometry, and simulated by a flexible numerical computation program. An analytical linearized model, based on convolution of Green’s fields, is expressed in multivariable state-space form, with its time-variant parameters identified in-process....
We consider a control constrained optimal control problem
governed by a semilinear
elliptic equation with nonlocal interface conditions.
These conditions occur during the
modeling of diffuse-gray conductive-radiative heat transfer.
After stating first-order necessary conditions, second-order
sufficient conditions are derived that account for strongly active sets.
These conditions ensure local optimality in an
Ls-neighborhood of a reference function
whereby the underlying analysis allows...
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
The paper deals with the moisture in the internal air of a modeling room. The problems connected with the undesired relative humidity of the indoor air are introduced, the reviewing of the hygric situation in the modeling room is described, the less or more precise models for relative humidity estimation depending on the influencing parameters are performed and the reasoning—when, why and how the particular models should be used, is added. As in particular hygric conditions some of the influencing...
A transmission problem describing the thermal interchange between two regions occupied by possibly different fluids, which may present phase transitions, is studied in the framework of the Caginalp-Fix phase field model. Dirichlet (or Neumann) and Cauchy conditions are required. A regular solution is obtained by means of approximation techniques for parabolic systems. Then, an asymptotic study of the problem is carried out as the time relaxation parameter for the phase field tends to 0 in one of...
We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
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