| Abstract: |
| This talk presents the construction of a strong solution to a one-dimensional free boundary problem modeling the penetration of a diffusing agent into rubber. The model consists of a parabolic equation describing the diffusion of the substance and an ordinary differential equation governing the motion of the free boundary. A central difficulty arises from the non-monotone boundary conditions at the moving edge, which occur because it is not known whether the concentration of the diffusing substance vanishes at the boundary. Due to this non-monotonicity, abstract evolution equation theory cannot be applied, and only weak solutions have been obtained so far. In this talk, we demonstrate that a strong solution can be constructed by employing the finite volume method, in which the spatial domain is divided into control volumes and discretized by enforcing conservation laws on each volume. |
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