作者:杨天浩，孙伟
Authors:YANGTianhao,SUNWei摘要:针对 一维区域上带有时间依赖系数的非齐次热传导方程的反初值问题 ,采用拟边值方法求解此问题。 首先根据分离变量法得到问题的解 ,并根据问题解的表达式构造了正则化解 ;其次在原问题的解满足某些先验条 件下 ,给出正则化参数选取的先验和后验方法 ,并在理论上严格证明了在此参数选取准则下 , 一 维热传导方程反初 值问题正则化解的收敛性 ;最后通过数值模拟表明 ,拟边值方法对于求解此反初值问题是有效和稳定的。
Abstract:Aiming at the problem of inhomogeneous backward heat conduction equation with time-dependent coefficients in a one- dimensional region , the quasi-boundary value method is used to solve this problem. Firstly , the solution of the problem is obtained by separating variables , and according to the expression of the solution of the problem , the regular solution is constructed; secondly , when the solution of the original problem satisfies some prior conditions , the priori and posteriori methods for the regularization parameter are given respectively , and the convergence of the regularization solution of the problem of one-dimensional backward heat conduction equation under this parameter selection criterion is strictly proved; finally , numerical simulation shows that quasi-boundary value method is effective and stable.

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