一类时间分数阶扩散方程反问题不适定分析及正则化解法
发布时间:2018-10-16 09:10
【摘要】:在许多工程物理问题中经常会用到时间分数阶扩散方程反问题,以需要测得物理内部的温度为例,对于这个问题,我们只能利用边缘温度的测量值去反演。本文主要研究的就是0γ1含有线性热源F ≠ 0的这类扩散方程反问题:这里定义的是Caputo意义下的分数导数:我们的反问题是:利用u(1,·)来反演u(x,t),x∈[0,1).我们通过严格的定理证明来说明这个问题是不适定的,因此我们需要对其进行正则化处理,为了保证研究顺利进行,我们研究不含热源即F = 0的情形:首先,我们假设初始值满足先验条件‖u(0,·)‖≤E,此外,设gδ(t)是测量值g(t)的扰动数据,且满足‖gδ-g‖≤ δ.因此只需考虑如下的反问题关于此类反问题的研究不是很多,本文中,我们提出了迭代方法和卷积方法来构造正则化格式,即傅里叶变换后的迭代方案和卷积方案并且给出了先验条件下迭代步数kk和卷积正则化参数α的选取方式和误差估计,即如果k=c[E/δ],可得到估计最后,我们会通过相应的数值例子来验证卷积正则化格式的可行性和有效性.
[Abstract]:The inverse problem of time fractional diffusion equation is often used in many engineering physics problems. Taking the internal temperature of physics as an example, we can only use the measurement value of edge temperature to inverse the problem. In this paper, we mainly study the inverse problem of the diffusion equation of 0 纬 1 with linear heat source F 鈮,
本文编号:2273893
[Abstract]:The inverse problem of time fractional diffusion equation is often used in many engineering physics problems. Taking the internal temperature of physics as an example, we can only use the measurement value of edge temperature to inverse the problem. In this paper, we mainly study the inverse problem of the diffusion equation of 0 纬 1 with linear heat source F 鈮,
本文编号:2273893
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