On one nonlinear problem of laser thermochemistry

The typical properties of the solutions of those equations describing the occurrence of several steady states, localization effects and complex changes in the temperature field caused by the thermal action of laser radiation on chemically active media are studied. Effective approximate methods are sought for finding the solutions. Surface heating of a metal specimen exposed to laser radiation is examined. The solution of a boundary problem to determine presence and number of steady-state solutions is investigated. The stability of the steady-state is analyzed by applying the theory of non-steady-state averaging to the boundary problem derived. The investigation is for the case of Gaussian distribution of the radiation intensity over the surface of the material; however, a number of important findings can also be obtained for an arbitrary distribution satisfying rather weak integrability conditions.