一种新的正则化方法求解热传导方程的侧边值问题

A New Regularization Method for Solving Sideways Heat Equations

考虑了四分之一平面内的热传导方程的侧边值问题,这类问题是严重不适定的.采用传统拟逆方法得到该问题的一个近似解,但发现它并不是一个正则化解.有趣的是,对解的分母项加以修正便可以得到侧边值问题的一个正则化解,进而提出了一种新的正则化方法,并分别给出先验和后验两种正则化参数选取规则下的H9lder型误差估计.数值实验验证了所提方法的可行性和有效性.

The seriously ill-posed sideways heat equations were considered in the quarter plane.The classical quasi-reversibility method was applied to acquire an approximate but non-regularized solution to the problem.Interestingly,a regularization solution to the sideways heat equation was obtained through modification of the denominator of the solution.Then,a new regularization method was proposed,and the H9 lder-type error estimates under a priori and a posteriori parameter choice rules were proved,respectively.Numerical experiments show the feasibility and effectiveness of the proposed method.