论文标题
部分可观测时空混沌系统的无模型预测
Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of weak solutions
论文作者
论文摘要
这项工作是一项关于核废料地质存储库长期安全性的一般研究的一部分。引入并研究了具有移动自由边界的扩散方程。该模型描述了与粘土石形成接触的碳钢罐表面涉及的一些机制。本文的主要目的是证明存在最大时间的问题解决方案。为此，引入了基于Wasserstein的距离的时间最小化运动方案。证明了该计划的解决方案。然后，使用先验估计值，结果表明，随着时间步长将其归零，这些解决方案将这些解决方案收敛至最大弱解，向自由边界模型。
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms involved in corrosion processes at the surface of carbon steel canisters in contact with a claystone formation. The main objective of the paper is to prove the existence of weak solutions to the problem which are maximal in time. For this, a time semidiscrete minimizing movements scheme based on a Wasserstein-like distance is introduced. The existence of solutions to the scheme is proved. Then, using a priori estimates, it is shown that as the time step goes to zero these solutions converge up to extraction towards a maximal weak solution to the free boundary model.
