摘要
对流一扩散方程中扩散系数反演问题,可以归结为一个特殊的非线性算子方程求解问题。通过对上述微分方程初边值问题(正问题)广义古典解的先验估计,给出了正问题解的正则性与扩散系数之间的依赖关系。并据此讨论了反问题提法的合理性,以及相应非线性算子的特性(连续性、弱闭性、紧致性)。
The problem of determining the diffusive coefficients can be formulated as one of solving a special nonlinear operator equation. The dependence of the gen-eralized classical solution (for the initial-boundary problem of convection-diffusion equation) on the diffusive coefficient was presented, by working out the priori estimations of the generalized classical solution. In view of this we discussed the rationality of the inverse problem, and considered the characteristics (continuity,compactness and weak closeness) of the corresponding nonlinear operator. Some results obtained here lay the foundation for theoretical analysis and numerical computation of the inverse problem.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
1992年第1期34-40,共7页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
国家自然科学基金
关键词
反问题
扩散系数
非线性算子
inverse problem
diffusion coefficient
nonlinear operator
