有界区域上非标准热方程只含有空间变量的热源识别反问题

The Inverse Problem of Identifying the Heat Source with Only Spatial Variable for the Non-standard Heat Equation in the Bounded Domain

探讨有界区域上一类含对流项热方程只含有空间变量的热源识别反问题.这类问题是不适定的,即问题的解不连续依赖于测量数据.利用拟可逆正则化方法,得到问题的一个正则近似解,并且给出正则解和精确解之间具有H?lder型的误差估计.

The inverse problem of determining a spacewise-dependent heat source is discussed for one-dimensional heat equation with convection term in the bounded domain.This problem is ill-posed,i.e.t,he solution does not de-pend continuously on the measurement data.A regular approximate solution of the inverse problem is obtained by the quasi-reversibility regularization method,and the H？lder type error estimation is got between the regularization solu-tion and the exact solution.