569 research outputs found
Existence, Uniqueness and Convergence of Simultaneous Distributed-Boundary Optimal Control Problems
We consider a steady-state heat conduction problem for the Poisson
equation with mixed boundary conditions in a bounded multidimensional domain
. We also consider a family of problems for the same
Poisson equation with mixed boundary conditions being the heat
transfer coefficient defined on a portion of the boundary. We
formulate simultaneous \emph{distributed and Neumann boundary} optimal control
problems on the internal energy within and the heat flux ,
defined on the complementary portion of the boundary of
for quadratic cost functional. Here the control variable is the vector .
We prove existence and uniqueness of the optimal control
for the system state of
, and
for the system state of , for each , and we give the
corresponding optimality conditions. We prove strong convergence, in suitable
Sobolev spaces, of the vectorial optimal controls, system and adjoint states
governed by the problems to the corresponding vectorial optimal
control, system and adjoint states governed by the problem , when the
parameter goes to infinity. We also obtain estimations between the
solutions of these vectorial optimal control problems and the solution of two
scalar optimal control problems characterized by fixed (with boundary
optimal control ) and fixed (with distributed optimal control
), respectively, for both cases and .Comment: 14 page
A free boundary model for oxygen diffusion in a spherical medium
The goal of this article is to find a correct approximated solution using a
polynomial of sixth degree for the free boundary problem corresponding to the
diffusion of oxygen in a spherical medium with simultaneous absorption at a
constant rate, and to show some mistakes in previously published solutions.Comment: 10 pages, 6 figures and 2 tables. Paper accepted, in press in Journal
of Biological Systems (2015
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