在外区域上具有不同初值的倒向热方程

Continuous Dependence on the Initial-time Geometry for Backward Heat Equation with Different Prescribed Data

基于Payne和Straughan关于具有相同初值的倒向热方程在外区域上的初值时刻几何的连续性研究技巧,研究了具有不同初始数据的倒向热方程在外区域上的不适定问题的解对初始时刻几何的连续依赖性.在一定条件下,用对数凸性的方法导出仅依赖于初始数据的连续依赖性的不等式.同时,可以应用数值模拟比较不同初始数据时解的图形.

By using the technique of Payne and Staughan in the studying of the continuous dependence on the initial-time geometry for the backward heat equation with given initial data,we studied the continuous dependence on the initial-time geometry in improperly posed problem for backward heat equation with different prescribed data.Under certain conditions,we drived an explicit continuous dependence inequality depending solely on the initial data by using the logarithmic convexity method.