A free boundary problem describing migration into rubbers -Quest for the large time behavior
A free boundary problem describing migration into rubbers -Quest for the large time behavior
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描述橡胶迁移的自由边界问题 - 探索大时间行为
DOI：
10.1002/zamm.202100134
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Muntean Adrian
中科院分区：
文献类型：
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作者：
Aiki Toyohiko;Kumazaki Kota;Muntean Adrian
在许多工业应用中，橡胶基材料通常与各种气态或液态的助溶剂或稀释剂一起使用。从理论上估计渗透深度以及材料内储存的扩散剂的量是有意义的。在这个框架中，我们证明了全局可解性，并探讨了具有非线性动力学条件的单相自由边界问题的解的大时间行为，该问题能够描述扩散剂向橡胶中的迁移。大时间行为的证明中的关键思想是从矛盾论证中受益，因为由于在固定边界处使用Robin边界条件，很难获得自由边界增长率的统一估计。
In many industrial applications, rubber‐based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time‐behavior of solutions to a one‐phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit from a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.