论文标题
扩展游戏型磁滞模型的解决方案的存在和特性
Existence and properties of solutions of extended play-type hysteresis model
论文作者
论文摘要
本文分析了[van Duijn＆Mitra（2018）]中提出的扩展游戏类型模型的良好性和特性，以通过多孔培养基将滞后纳入不饱和流中。当正则化时，该模型将还原为非线性退化抛物线方程，并与普通的微分方程相连。据我们所知，这具有有趣的数学结构，仍然没有探索。使用Rothe的方法显示了模型非分类版本的解决方案的存在。对于解决方案证明了相当于最大原理的等效原理。假设初始条件远离堕落点，则显示对退化情况的溶液的存在。最后，表明如果存在未注册情况的解决方案，则将其包含在物理一致的边界内。
This paper analyses the well-posedness and properties of the extended play-type model which was proposed in [van Duijn & Mitra (2018)] to incorporate hysteresis in unsaturated flow through porous media. The model, when regularised, reduces to a nonlinear degenerate parabolic equation coupled with an ordinary differential equation. This has an interesting mathematical structure which, to our knowledge, still remains unexplored. The existence of solutions for the non-degenerate version of the model is shown using the Rothe's method. An equivalent to maximum principle is proven for the solutions. Existence of solutions for the degenerate case is then shown assuming that the initial condition is bounded away from the degenerate points. Finally, it is shown that if the solution for the unregularised case exists, then it is contained within physically consistent bounds.
