The quasi-reversibility method to solve the Cauchy problems for parabolic equations
The quasi-reversibility method to solve the Cauchy problems for parabolic equations
复制标题
求解抛物方程柯西问题的准可逆性方法
DOI：
10.1007/s10114-013-1735-x
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
B. Guo
中科院分区：
文献类型：
--
作者：
Jing Li;B. Guo
本文一方面利用常规的拟可逆性方法得到了QT子域上抛物型方程Cauchy问题的近似解的误差估计，并对边界条件进行了严格的限制.另一方面，通过弱化对测量数据的约束条件，将最优化中的对偶方法与拟可逆方法相结合，求解了噪声数据下的抛物型方程Cauchy问题。利用这种方法，我们可以得到拟可逆方法中所需的正则化参数λ，并在振幅噪声δ趋于零时得到近似解的收敛速度。
In this paper, on the one hand, we take the conventional quasi-reversibility method to obtain the error estimates of approximate solutions of the Cauchy problems for parabolic equations in a sub-domain ofQTwith strong restrictions to the measured boundary data. On the other hand, weakening the conditions on the measured data, then combining the duality method in optimization with the quasi-reversibility method, we solve the Cauchy problems for parabolic equations in the presence of noisy data. Using this method, we can get the proper regularization parameterɛthat we need in the quasi-reversibility method and obtain the convergence rate of approximate solutions as the noise of amplitudeδtends to zero.