Parameter identification and application of a distributed parameter coupled system with a movable inner boundary

In this paper, we establish a distributed parameter coupled system concerning Arctic sea ice temperature field, in which the ice thickness is regarded as a movable inner boundary of the space domain. The existence and continuity of the weak solution to the coupled system are proved. According to the measured data, we establish a parameter identification model with the ice thickness as control variable and the coupled system as constraints. Finally, an optimization algorithm is constructed on the basis of non-overlapping domain decomposition method and semi-implicit difference scheme. Through numerical calculation, we obtain the characteristics of the ice thicknesses and the ice temperatures.