具有不同初值的前向热方程对初始时刻几何的连续依赖性

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

研究了具有不同初始数据的前向热方程不适定问题的解对初始时刻几何的连续依赖性.对这类不适定问题数据的稳定性研究是由在物理过程中无法对t=0时刻所有数据在瞬间测定而产生的初始时刻几何误差引起.当对方程的解进行适当限制后,可以利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,推出它的H lder稳定性,从而得到问题解的连续依赖性.

In this paper we study the continuous dependence on the initial-time geometry in improperly posed problem for forward heat equation with different prescribed data.This study were caused by the errors in characterizing the initial-time geometry.Because we can't measure all the data at the same instant of time during the physical processes.If the class of admissible solutions is suitably restricted,an explicit inequlity depending solely on data will be derived by logarithmic convexity method. Then we can obtain its Hlder stability and solutions′s continuous dependence on the data.