Comparison theorem for embrasures in the integral theory of fire (Q1935414)

The author studies a system consisting of one first-order differential equation and one algebraic equation \[ \begin{gathered} \frac{dx}{d\tau}=-\tau^2x+\Phi(1-x)^{3/2}\beta(\xi),\\ \tau^2+\Phi(1-x)^{1/2}(\beta(\xi)-x^{-1/2}\gamma(\xi))=0, \end{gathered} \] where \(\Phi\) is a numerical parameter. This system has applications in theory of fires in rooms. The author obtains comparison theorems which allow them to deduce a relationship between different solutions and thus to compare the values of dangerous factors arising in fires.