Modeling an optimal temperature field in a thermoplastic medium
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.
scientific article; zbMATH DE number 1646392