论文标题
非线性偏微分方程中参数识别问题的一种新的正则化方法
A new regularization method for a parameter identification problem in a non-linear partial differential equation
论文作者
论文摘要
我们考虑与准线性椭圆形的neumann边界价值问题有关的参数识别问题，涉及参数函数$ a（\ cdot）$和解决方案$ u（\ cdot）$，其中问题是在间隔$ i：= g（γ）上确定$ a（\ cdot）$，从解决方案上$ c $ c $ c cy $ u（\ cd）$（\ cd）$ u（\ cd），在域的边界上，问题的$ω\ subseteq \ mathbb {r}^3 $和$ g $是连续的函数。为了获得稳定的近似解决方案，我们考虑了新的正则化方法，该方法给出了与近期文献中所考虑的经典Tikhonov正则化相似的误差估计。
We consider a parameter identification problem related to a quasi-linear elliptic Neumann boundary value problem involving a parameter function $a(\cdot)$ and the solution $u(\cdot)$, where the problem is to identify $a(\cdot)$ on an interval $I:= g(Γ)$ from the knowledge of the solution $u(\cdot)$ as $g$ on $Γ$, where $Γ$ is a given curve on the boundary of the domain $Ω\subseteq \mathbb{R}^3$ of the problem and $g$ is a continuous function. For obtaining stable approximate solutions, we consider new regularization method which gives error estimates similar to, and in certain cases better than, the classical Tikhonov regularization considered in the literature in recent past.
