Abstract:
Low-temperature effects on biological tissues are accompanied by phase transitions that lead to the appearance of moving phase boundaries. Mathematical modeling of such processes is a complex task requiring special solution methods. The proposed paper considers the possibility of using asymptotic integration to solve the problem with free boundaries arising from low-temperature effects on biological tissues in order to simplify models and obtain analytical and quasi-analytical approximations that allow analyzing the influence of various parameters on the dynamics of the process. In this paper, we consider a new formulation of a two-dimensional problem with free boundaries, and obtain a simpler two-dimensional stationary Stefan problem.
Keywords:free boundary, asymptotic integration, phase transitions, low-temperature exposure, asymptotic decomposition, zero approximation, equation of the first approximation.
