Modeling an optimal temperature field in a thermoplastic medium
type: Item
instance of: scholarly article
zbMATH Open document ID: 0970.80006
author: Oleksandr Yu. Grishchenko
author: L. I. Potapenko
author: O. B. Stelia
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 1646392
zbMATH Keywords: simulation
zbMATH Keywords: optimal temperature field
zbMATH Keywords: thermoplastic medium
zbMATH Keywords: hidden image
zbMATH Keywords: polymeric semiconducting film
MaRDI profile type: Publication
title: Modeling an optimal temperature field in a thermoplastic medium
published in: Zhurnal Obchyslyuval'noïta Prykladnoï Matematyky
review text: The authors consider the problem of creation of the optimal temperature field of a medium for visualization of hidden images using thin polymeric semiconducting films. This problem is formulated as an optimal control problem for the heat equation and then it is reduced to an optimization problem for the following stationary equation: NEWLINE\[NEWLINEJ(q)=\int\limits_{0}^{l_1}(T(x,l_2;q)-T_{z}(x))^2dx\to\min; NEWLINE\]NEWLINE NEWLINE\[NEWLINE {\partial\over\partial x}\left(\lambda {\partial T\over\partial x}\right)+{\partial\over\partial y}\left(\lambda {\partial T\over\partial y}\right)+q(x)\delta(y-d)=0; \quad (x,y)\in (0,l_1) \times(0,l_2);NEWLINE\]NEWLINE with the boundary conditions \(\left.{\partial T\over\partial x}\right|_{x=0}= \left.{\partial T\over\partial x}\right|_{x=l_1}\), \(T|_{x=0}=T|_{x=l_1}\) and the conjugacy conditions in the location \(y=d\) of electrically conducting films \(T|_{y=d-0}=T|_{y=d+0}\), \(\left.\lambda{\partial T\over\partial x}\right|_{y=d-0}- \left.\lambda{\partial T\over\partial x}\right|_{y=d+0}=q(x)\), where \(\lambda\) is the heat conducting coefficient; \(q(x)\) is the thermal equivalent of the power of the electric current impulse; \(T_{z}(x)\) is the given temperature on the thermoplastic layer \(y=l_2\). For the solution of the obtained problem the gradient method is used.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1646392