| Abstract: |
| We consider a free boundary problem for a system of two parabolic equations on the one-dimensional space interval. The problem has been proposed as a mathematical model for a baking bread process in a hot oven. In the model we assume that the region consists of crumb, crust, and the evaporation front. For the model, we add a free boundary condition obtained from the energy conservation law. The unknown functions of our problem are the position of the evaporation front, the temperature field, and the water content. For solving this problem we observed two difficulties that the growth rate of the free boundary contains the water content and the boundary condition for the water content depends on the unknown temperature at the boundary. For these issues, we can establish existence of a strong solution locally in time and its uniqueness under high regularity assumptions on the initial data. Moreover, based on analysis for stationary solutions, we present the behavior result on the free boundary in this talk. The key of the proof is that a comparison principal for the solutions holds, even if the latent heat coefficient depends on time and lacks differentiability with respect to the time variable. |
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