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An accurate application of the integral method applied to the diffusion of oxygen in absorbing tissue

机译：积分法在吸收组织中氧气扩散中的准确应用

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Accurate integral methods are applied to a one dimensional moving boundary problem describing the diffusion of oxygen in absorbing tissue. These methods have been well studied for classic Stefan problems but this situation is unusual because there is no condition which contains the velocity of the moving boundary explicitly. This paper begins by giving a short time solution and then discusses some of the previous integral methods found in the literature. The main drawbacks of these solutions are that they cannot be solved from t = 0 and also cannot determine the end behaviour. This is due to the non-uniform initial profile which integral methods typically fail to capture. The use of a novel transformation removes this non-uniformity and, on applying optimal integral methods to the resulting system, leads to simple and yet very accurate approximate solutions that overcome the deficiencies of previous methods.
机译：精确的积分方法应用于描述吸附组织中氧气扩散的一维运动边界问题。对于经典的Stefan问题，已经对这些方法进行了充分的研究，但是这种情况并不常见，因为没有明确包含运动边界速度的条件。本文首先给出了一个简短的解决方案，然后讨论了文献中发现的一些先前的积分方法。这些解决方案的主要缺点是无法从t = 0开始求解，也无法确定最终行为。这是由于整体方法通常无法捕获的初始轮廓不均匀所致。使用新颖的变换可消除这种不均匀性，并且在将最佳积分方法应用于所得系统时，可得出简单而又非常准确的近似解决方案，从而克服了先前方法的不足。

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