论文标题
在移动的薄域及其极限方程式中热方程式的经典解决方案的错误估计
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation
论文作者
论文摘要
我们考虑了在给定的闭合移动超表面周围移动的薄域中热量方程的Neumann型问题。本文的主要结果是对于薄域问题的经典解决方案的SUP-NORM中的错误估计，以及在热量方程的薄膜限制中出现的移动性超曲面上的极限方程。为了证明误差估计，我们根据最大原理显示了对薄域问题的经典解决方案的先验估计。此外，我们基于薄域问题的渐近扩展，构建了从经典解决方案到极限方程的薄域问题的合适近似解决方案，并将统一的先验估计值应用于近似解决方案的差异和对薄域问题的经典解决方案的差异。
We consider the Neumann type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a priori estimate for a classical solution to the thin domain problem based on the maximum principle. Moreover, we construct a suitable approximate solution to the thin domain problem from a classical solution to the limit equation based on an asymptotic expansion of the thin domain problem and apply the uniform a priori estimate to the difference of the approximate solution and a classical solution to the thin domain problem.
