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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...
We present in this work a numerical study of a problem governed by Navier-Stokes
equations and heat equation. The mathematical problem under consideration is obtained by
modelling the natural convection of an incompressible fluid, in laminar flow between two
horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed
to be greater than the outer one. The numerical simulation of the flow is carried out by
collocation-Legendre...
We analyze two numerical schemes of Euler type in time and C0
finite-element type with -approximation in space for
solving a phase-field model of a binary alloy with thermal
properties. This model is written as a highly non-linear parabolic
system with three unknowns: phase-field, solute concentration and
temperature, where the diffusion for the temperature and solute
concentration may degenerate.
The first scheme is nonlinear, unconditionally stable
and convergent. The other scheme is linear...
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