Stationary heat distribution in an infinite strip

The problem of continuous dependence of stationary heat propagation on temperature and heat flux in an infinite strip has been considered. A class of approximate solutions has been constructed in the form of special series and a regularizing operator, which has the property of being stable to small deviations in the values of temperature and heat flux functions. In this case, the choice of the smoothing function and conditions for matching the regularization parameter with the error play an important role. (author)