摘要
讨论了一个一维逆热传导问题，利用正则化方法得到了表面热流的近似解．在假定（未知）精确解属于Ｈα（Ｒ），α≥１２条件下，给出了阶为１／（ｌｎ１ε）２α的误差估计，其中ε为测量误差的Ｌ２界．解决了同类研究中的一个遗留问题．
In
several engineering contexts there is sometimes a need to determine the surface temperature
or surface heatflow from interior observations. This problem is well known to be severely ill
posed. Such a dimensional inverse heat transfer problem is considered. Using the
regularization method and assuming the (unknown)exact solution is in H α(R), α≥1/2 , we
give an approximate solution of surface heatflow and error estimate of the order 1/( ln (1ε))
2α for ε>0 , where ε>0 is a bound on the measurement error. The question left over in
the research of the same kind is resolved.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
1999年第1期18-24,共7页
Journal of Lanzhou University(Natural Sciences)
基金
甘肃省自然科学基金
关键词
热传导方程
不适定问题
正则化
误差估计
inverse problem
heat conduction
equation
ill posed problem
regularization method
error estimation
