一类二维热传导方程的反源问题

Inverse source problem for a kind of two-dimensional heat conduction equation

热传导方程反源问题是工程和自然科学中一类非常重要的反问题,需要通过数学方法求解未知源项。本研究针对源项仅依赖时间变量的矩形域Ω=[0,π]×[0,π]■R2上的反演问题进行分析,证明了反源问题的唯一性和条件稳定性,并给出了Tikhonov正则解与精确解的误差估计。

In engineering and the natural sciences,inverse source problem for the heat conduction equation is an important class of inverse problems.It needs to solve the unknown source items through mathematical methods.The inversion problem on the rectangular domainΩ=[0,π]×[0,π]■R^(2) where the source term only depends on the time variable is studied.The uniqueness and conditional stability of the inverse source problem are proved,and the convergence estimates between the exact solutions and the Tikhonov regularized solutions are presented.