论文标题
局部存在的解决方案解决了一个自由边界问题，描述了迁移到橡胶中具有破坏效果
Local existence of a solution to a free boundary problem describing migration into rubber with a breaking effect
论文作者
论文摘要
我们考虑一个一维自由边界问题，描述了扩散剂向橡胶的迁移。在我们的环境中，自由边界表示扩散区域的前面划界的位置。该区域的生长速率由一个普通的微分方程描述，其中包括破坏扩散区域的生长的效果。在这种特定情况下，假定断裂机制是对太快扩散穿透的高弹性反应。在最近的作品中，我们考虑了类似的自由边界问题，将扩散剂渗透在橡皮图中进行建模，但没有试图处理破坏或加速发生的自由边界的可能性。对于简化的设置，我们能够展示全局的存在和独特性以及对我们配方的相应解决方案的大型行为。由于这里的断裂效果包含在自由边界条件下，因此我们先前的结果不再适用。确保解决方案存在的主要数学障碍是自由边界的非单调结构。在本文中，我们确定了通过破坏效果的自由边界问题的弱解决方案的存在和独特性，并明确给出了自由边界可以达到的最大值。
We consider a one-dimensional free boundary problem describing the migration of diffusants into rubber. In our setting, the free boundary represents the position of the front delimitating the diffusant region. The growth rate of this region is described by an ordinary differential equation that includes the effect of breaking the growth of the diffusant region. In this specific context, the breaking mechanism is assumed to be the hyperelastic response to a too fast diffusion penetration. In recent works, we considered a similar class of free boundary problems modeling diffusants penetration in rubbers, but without attempting to deal with the possibility of breaking or accelerating the occurring free boundaries. For simplified settings, we were able to show the global existence and uniqueness as well as the large-time behavior of the corresponding solutions to our formulations. Since here the breaking effect is contained in the free boundary condition, our previous results are not anymore applicable. The main mathematical obstacle in ensuring the existence of a solution is the non-monotonic structure of the free boundary. In this paper, we establish the existence and uniqueness of a weak solution to the free boundary problem with breaking effect and give explicitly the maximum value that the free boundary can reach.
