一类热传导方程多点源反演的唯一性和稳定性

Uniqueness and Stability in Determining the Point Sources for a Heat Conduction Equation

在第一类Dirichlet边界条件下,研究了由表面热流密度来反演热传导方程多点源的唯一性和稳定性,即反演点源个数n、热源强度组合系数αi、点源位置si的唯一性和反演点源位置si的稳定性。利用热变换方法将热传导方程反问题转化为等价的双曲型方程反问题,然后通过分析等价的双曲型方程反问题得到原反问题的唯一性和条件稳定性结论。

Under the Dirichlet boundary conditions, this paper is concerned with the uniqueness and the stability in determining the point sources from the boundary heat flux. We study the uniqueness of the numbers of point sources, the intensity coefficients and the locations, and the conditional stability of the source locations. The inverse heat source problem is transformed into an equivalently inverse problem of hyperbolie equation by the heat transformation. Then, the uniqueness and conditional stability are obtained by the results of the equivalently inverse hyperbolic source problem.